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```Ill A

MAP AND AERIAL

(NAVMC— 3001)

1944

Published : —
For Instructional Purposes Only.

MARINE CORPS SCHOOLS

MARINE BARRACKS, QUANTICO, VIRGINIA

20 Mat, - Zl ->£

SECTION 1
GENERAL

Paragraph Page

Purpose 1 1

Scope 2 1

Necessity for Training 3 1

Maps and Aerial Photographs 4 1

Map Classification 5 2

Limitations of Maps 6 2

Marginal Information 7 3

Overlays 8 4

SECTION 2

Introduction . 9 7

Fractions .-."'. 10 7

Ratio and Proportion ' 11 9

Fractional Equations 12 9

Decimals 13 10

Parallels 14 12

The Circle 15 13

Working Problems 16 14(a)

Navy Time 17 14(a)

Table of Equivalents 18 14(b)

SECTION 3

CONVENTIONAL SIGNS AND MILITARY SYMBOLS

Conventional Signs 19 15

Military Symbols 20 18

SECTION 4

MAP MEASUREMENTS

Scales

Distance

Time

Relation Between Distances and Areas on Maps of

Different Scales

Determination of Scale of Map and Construction of

Graphic Scale

Time-Distance Scales

Ill A— i

21

19

22

19

23

21

24

22

25

24

26

28

SECTION 5

DIRECTION

Need for Direction

Units of Angular Measure

Base Direction

Declination

Use

Azimuth

Bearing

Local Magnetic Attraction

Determination of Direction by Field Expedients

Protractor

Use of Protractor

Locating Point by Intersection and Resection .

Paragraph Page

27

31

28

31

29

32

30

33

31

38

32

38

33

41

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42

35

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36

45

37

46

38

47

SECTION 6
COORDINATES

General .>. .

Polar Coordinates

Rectangular Coordinates .
Scale of Proportional Parts
Geographic Coordinates . .

Military Grid System

Continental System .......

Equatorial System

Military Grid

Coordinate Scale

Thrust Line

39

51

40

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41

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42

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46

m

47

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68

49

70

SECTION 7
ELEVATION AND RELIEF

General

Contours

Contour Interval

Elevations of Important Features

Logical Contouring

Determination of Elevation

Ridge Lining and .Stream Lining .

50

73

51

73

52

78

53

78

54

78

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82

56

83

III A— ii

SECTION 8
SLOPE, PROFILE, AND VISIBILITY

Paragraph Page

Slope 57 87

Slope in Percent 58 87

Slope in Mils 59 87

Slope in Degrees 60 89

Slope Between Two Points on Map 62 89

Average Slopes 63 89

Profile 64 89

Visibility 65 92

SECTION 9

General

Orientation

Finding Observer's Position on Map

Two Point Intersection

Traverse

Compass .

66

97

67

97

68

100

69

111

70

113

71

114

SECTION 10
AERIAL PHOTOGRAPHS

General 72 119

Oblique 73 121

Vertical 74. 125

Identifying Terrain Features 75 125

Orientation 76 131

Atlas Grid 77 133

Scale 78 134

Mosaic 79 137

Photomaps 80 137

Marginal Data 81 137

Care in Use of Photomaps 82 137

Aids in Use of Photomaps 83 138

Methods of Reproduction 84 138

Stereovision 85 139

III A— iii

SECTION 11
HYDROGRAPHIC CHARTS

Definition

Sources from which Charts are Obtained

Types

Cprrection

Conventional Signs

Factor to be Considered in Making a Chart Study . .
Limitations

SECTION 12

Paragraph

Page

86

141

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141

88

141

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142

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144

92

144

93

146

FOREIGN MAPS

Foreign Maps 94 147

British Grid System 95 149

French Geographic Grid 96 151

III A— iv

LIST OF ILLUSTRATIONS

Figure Page

Declination Diagram and Graphic Scales 1 4

Angles Formed by a Line Intersecting Parallel Lines 2 12

The Circle 3 13

Diagram of 1 Mil -4 14

Common Conventional Signs 5a.&5b. 16-17

Using Graphic Scale to Measure Distance 6 20

Measuring Distance Along a Winding Road 7 22

Relation Between Distances and Areas on Maps of

Different Scale 8 23

Construction of Graphic Scales 9a. & 9b. 27

Time-distance Scales 10 29

Units of Measurement 11 31

Declination 12 33

Isogenic Lines 13 35

Determining Difference in Direction Between Grid

and Magnetic North 14 37

Diagram Illustrating Reason for Grid Declination . . 15 39
Example of Relationship Between Three Base Direc-
tions on a Map, Showing Corresponding Azi-
muths and Back Azimuths of Line OA 16 40

Back Azimuths 17 41

Diagram Indicating Relation Between Bearing and

Azimuth 18 42
Typical Direction Expressed as Azimuth and as

Bearing 19 43

Military Protractors 20 45

Using Protractor to Measure Map Azimuth 21 46

Plotting Azimuths 22 47

Location by Intersection and Resection 23 48

Polar Coordinates: BM 38, Accotink (Village) Dis-
tance 1,800 Yards on Grid Azimuth 22° 30' . 24 52
Rectangular Coordinates: BM 38, Accotink (Village)
1,500 Yards East Magnetic. 1,100 Yards North

Magnetic 25 54

Measuring Between Parallels 26 56

Geographic Coordinates: Latitude 38°42'20"N.,

Longitude 77°13'30"W 27 59

Designation of Military Grid Systems 28a. & 28b 62-63

Coordinates 29 67

Plotting Point With Coordinate Scale 30 69

Improvising a Coordinate 31 <jq

Thrust Line 32 7^

Side View of Hill 33 74

Oblique View of Hill 34 74

Top View of Hill 35 75

Hill Shown by Contours 36 75

Characteristics of Contours 37 77

III A— v

38

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39

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40

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54

104

LIST OF ILLUSTRATIONS (Continued)

Figure Page

Method of Drawing Contours by Interpolation on
Drainage Net Where Elevations Are Given . . .

Determination of Elevation on Contoured Map

Ridge and Drainage Lines

Determination and Expression of Slope Between Two

Points "A" and "B" on Map

Construction of a Profile

Determination of Visibility by Profile Method

Determination of Visibility by Hasty Profile Method

Orienting Map by Inspection

Orientation of Maps by Compass

Orienting Map by Means of Distant Point

Locating Position on Map by Inspection

Location of Observer's Position on Map by Striding

or Estimating Distance When Along Road ....
Location of Ones Position on Map by Resection

Location of Ones Position on Map by Resection When

Along Road, Using Compass and Protractor ....

Location of Ones Position on Map by Resection

From Two Distant Points (Graphic Method) . . 55 106

Location of Ones Position on Map by Resection
From Two Distant Points, Using Compass and

Protractor 56 107

Three Point Resection in the Field 57 109

Locating Position on a Map by Tracing Paper

Overlay 58 110

Location on Map of Distant Point by Intersection,

Using Compass and Protractor 59 112

Location on Map of Distant Point by Intersection

(Graphic Method)

Prismatic Compass

Use of Compass Dial

Relative Shape of Area Covered by Oblique Photo-
graph Compared to Photograph Itself

Low Oblique

Vertical Photograph

Identifying Terrain Features

Placing Magnetic North Line on Aerial Photograph .

Atlas Grid and Marginal Data

Diagram Showing Relation of Scale, Focal Length

and Lens Height

British Grid System

Japanese Map Symbols

Ill A— vi

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152

SECTION 1
GENERAL

1. Purpose. — The purpose of this manual is to present in
simplified form necessary information for instruction of all
military personnel in elementary map and aerial photograph

2. Scope. — a. This manual covers elementary map read-
ing, including conventional signs and military symbols, dis-
tances and scales, directions and azimuths, coordinates, relief,
slopes, profiles and visibility, map reading in the field, and
aerial photograph reading, to an extent sufficient to permit
aerial photographs, and aerial mosaics.

3. Necessity for Training. — Modern warfare makes it es-
maps and aerial photographs. The detailed study of maps
assists higher commanders in arriving at their tactical deci-
sions. In transmitting orders, they often will use maps which
outline their plans to their subordinate commanders. In order
to carry out these orders intelligently, the subordinate com-
manders must be able to read any type of map involved. Maps
are used to move various combat units to their assigned posi-
tions and to identify their boundaries, areas, and objectives.
The supporting fires of many weapons are usually controlled
by use of map data. Frequently soldiers will be given individ-
ual missions requiring them to travel long distances with only
a map as a guide. Since aerial photographs or photomaps
made from aerial photographs are constantly being used as
maps or to supplement maps, the necessity for training in
their use is equally important as training in use of maps.

4. Maps and Aerial Photographs. — A map is a graphic,
conventionalized representation to scale of a portion of the
surface of the earth as a plane surface. Not all maps or map
substitutes, however, satisfy all the requirements of this
generalized definition. Types of maps or aerial photographs
generally issued to troops will vary a great deal depending
on location of operations. Large scale topographic maps desir-
able for tactical operations of small units exist for only limited
areas, so some of lesser accuracy normally may be expected.
These may range from ordinary automobile road maps to
some type of map substitute. Various types of maps and map
substitutes which may be encountered are :

a. Maps compiled from existing maps. — Normally
troops may expect to be furnished some type of map hastily
compiled from such maps as exist at the outbreak of hostili-
ties. These maps may vary from crude, small scale maps such
as ordinary automobile road maps, to accurate, large scale,

III A— l

topographic maps. Large scale topographic maps suitable
for tactical operations of small units may be expected only in
isolated areas of limited size.

b. Map substitutes. — This is a general term used to
designate substitute maps that may be produced in a few
hours. The map substitutes may consist of direct reproduc-
tion of wide coverage aerial photographs, photomaps or
mosaics, or of provisional maps. The term "photomap" is
used as a general term to describe reproductions of various
types of aerial photographs. A provisional map is produced
by compiling existing map detail or by tracing information
from aerial photographs.

c. Battle maps. — This is a map prepared normally
from aerial photographs on a scale of 1 :20,000, which is suit-
able for tactical and technical needs of all arms. Normally,
this type of map would not be made available for any exten-
sive area until at least 3 weeks after outbreak of hostilities.

5. Map Classification. — Military maps are generally classi-
fied according to scale. The general types are :

a. Small. — Maps of small scale varying from 1:1,000,-
000 to 1 : 7,000,000 are needed for general planning and strate-
gical studies by the commanders of large units.

b. Intermediate. — Maps of intermediate scale, normally
from 1:200,000 to 1:500,000 are required for planning opera-
tions, including movements, concentration, and supply of
troops.

c. Medium. — Maps of a medium scale, that is, from
1:50,000 to 1:125,000 are needed for strategical, tactical, and
administrative studies by units ranging in size from a corps
down to a regiment. The compiled map described in paragraph
4a is of this type.

d. Large. — Large scale maps, generally of a scale not
greater than 1 : 20,000 are intended for this technical and tac-
tical battle needs of field artillery and infantry. Paragraph
4c describes this type.

6. Limitations of Maps. — A spherical surface cannot be
reproduced as a plane surface with absolute accuracy, just as
the skin of half an orange cannot be flattened without splitting
the rind; therefore, any representation is an approximation
only with limitations depending on the projection used. Most
military maps use a type of prejection known as poly conic be-
cause it limits the distortion involved. Due to changes in
atmospheric conditions, the paper on which a map is printed
may shrink or expand. During the printing process, one litho-
graphic plate is used for each color, hence any amount of
slipping with relation to the plate may make considerable
difference in the relative position of a contour and any other
symbol on the map. For these reasons two copies of the same

III A— 2

edition of a map may have considerable variance. Distances,
coordinates, or elevations taken from one map will not agree
to the last decimal or foot with those taken from another.
Radical differences, however, indicate errors in location or in
obtaining data.

Survey methods of mapping are slow, expensive, and
cumbersome. Their degree of accuracy is never all that might
be expected. Seldom do they meet military requirements,
particularly when fire control problems are involved. More-
over, it is interesting to note that only 1% of the United
States is mapped to a scale of 1:20,000, the minimum requisite
for artillery usages ; only 12% is mapped to a scale of 1 : 62,500,
the standard for tactical usage; and 85% is either inade-
quately mapped or the maps are so old or were made by such
crude methods that they do not satisfy modern needs. For
these reasons, recourse is had to aerial photographs, which
will be studied later.

7. Marginal Information. — All military maps and most
other maps show additional information along their margins.
This is sometimes called the "map legend" and while it varies
in detail and degree a study of the margins will generally
reveal at least the following :

a. The name or title of the sheet and the general area
covered.

b. The scale of the map expressed in several ways.

c. The direction of true, magnetic, and grid (if any)
north lines.

d. The organization that made or supervised the origin-
al survey or revision.

e. The date of the original survey and subsequent re-
visions.

f . The organization issuing the map.

g. Adjacent sheet in the same series if any.
h. Unusual conventional signs or symbols.

i. The contour interval.

j. The projection used.

All these things tend to indicate the uses and limitations
as well as the accuracy and reliability of the map under con-
sideration and should be carefully studied and evaluated before
using the map.

Ill A— 3

True and magnetic north (grid north
omitted when grid not shown).

Type of standard scale

APPROXIMATE DECLINATION 1933
ANNUAL MAGNETIC CHANGE 4'-30"
INCREASE

miles

1 2

1 SCQle 90,000 2

3 A

IOOO 1000

2000 3000 4000

5000

6000 7000 ya

I i

W ^1 l-l U-l M 1

1 2 3

4

5 kilometers

GontouT interval 25 ft.
go. //4B Datum is mean sea level.

Figure 1. — Decimation diagram and graphic scales.

Marginal information should appear on all standard military maps. The
above are examples of such marginal information.

8. Overlays. — An "overlay" is a diagram normally com-
posed of special military symbols drawn on transparent paper
which has for its purpose the pictorial representation of mili-
tary dispositions or situations at a given time. Its use is
necessitated by the following facts: (1) We must conserve
our maps because we shall never have an unlimited supply;
(2) information coming from a great number of subordinate
units in the form of overlays can easily be consolidated on
the map of the higher unit and thus give a complete picture
of that unit or of enemy activities; and (3) through the use
of hastily-produced overlays, detailed information or instruc-
tions can be rapidly disseminated among subordinate units.
This system reaches its peak of efficiency when orders are
supplemented by operations overlays. A brief description of
overlays will make their use within the capabilities of the
new student as well as the person of considerable experience.
Remembering that an overlay is used for the purpose of
conserving both time and effort, it is to be noted that no
information is placed on the overlay which already appears
on the original map. Information of the terrain or of man-
made permanent features are only placed on an overlay when
necessary for the correction of the map with which it is to be
used, such as showing new buildings that have been erected
or a shore line that has shifted since the time the map was
originally compiled. Hence, there will normally be shown
only military dispositions, field fortifications, establishments,
schemes of maneuver, etc. These are all represented by
means of authorized military symbols with the exception
that when no approved symbol exists it is permissible to
devise symbols so long as an explanation of them is given in
the legend of the overlay.

Ill A— 4

In order that an overlay may be of use to a person
other than the one constructing it, its purpose must be known
and there must be some means of applying it accurately to
any map similar to the one from which it was taken. This
is done by giving the following information in the legend : Map
or chart used, title, date of issue, scale; title of the organi-
zation submitting the overlay; place, date, and time of issue
of the overlay; purpose of the overlay or designation of the
order which it is to accompany. For exact application to
another map it is necessary to inscribe at least two registra-
tion "ticks" on the overlay. These are in the form of small
crosses which indicate the intersection of grid lines on the
map. They are numbered with the corresponding numbers
of the military grid, thus fixing the coordinates of two points
on the overlay, and are normally placed near two diagonally
opposite corners of the overlay. Maps, charts, and aerial
photographs that have no grid will often be adapted to use in
the Marine Corps. Overlays from these can be registered by
showing the location of prominent features, such as buildings,
road junctions, or a portion of the coast line. In conclusion,
the student must remember that while another person might
be able to divine information that has been omitted from the
legend, an overlay is utterly useless if it does not contain
marks of registration.

Ill A— 5

SECTION 2

9. Introduction. — A knowledge of elementary mathematics
is sufficient for the requirements of map reading. This section
contains those simple principles of elementary mathematics
which should be reviewed prior to the study of this text.

10. Fractions. — a. A fraction is merely a way of indicating

1 1

division. Thus the simple fraction — means 1 -f- 4 ; — , 1 -^ 62 ;

4 62

41
and — , 41 -f- 13. Thus the fraction sign ( — ) indicates divi-

13
sion.

b. Complex fractions consist of a whole number over

2 6

a fraction , a fraction over a whole number , or of a

1 5

4

fraction over a fraction . Complex fractions can always

4

7

be reduced to ordinary fractional form by merely performing
the division indicated. First, the complex fraction is written

4 3 4

so as to show division; thus, = : . Then the de-

_4_ 4 7

7

nominator, (the lower section of the fraction) is inverted

4 7

(turned upside down), thus — becomes — . The numerator

III A— 7

(upper section) of the fraction is then multiplied by the in-

3 7 3X7
verted denominator (lower section) ; thus — X — =

4 4 4X4
21 21

— , thus our answer — is the simple fractional form equal to
16 16

_3_

4
the complex fraction

_4_

7

Examples of complex fractions reduced to simple form :

2 1 4 8

= 2 -^ = 2X— = — = 8.

1_ 4 11

4

8
(A number divided by one equals the number, thus — = 8).

1
1_

6 1 1111

5 6 6 5 6X5 30

(To invert a whole number, write it as a fraction with

1
one as the numerator, thus 5 inverted = — ).

5
1

6227

1

1

1 4283

4283

= X — -

1

6227

4283

6227 1

6227

4283

c. The value of a fraction remains unchanged if both
the numerator and the denominator are multiplied or divided
by the same number, e.g.

J_

1^3 3

1 1X2 2 2-^-2 1

1

4 4X2 8 8-f2 4

4

13 3 3-3 1

3 4 ""~12~ 12-T-3 4

III A— 8

4-^3 _4
3

Thus, if you wish to reduce a fraction to a form in
which its numerator is one, divide both the numerator and

4

the denominator by the numerator, e.g., to reduce — to a

24

4 4-^4 1

fraction with a numerator of one : — = = — .

24 24 ^ 4 6

11. Ratio and Proportion. — a. Fractions may be used to
represent the ratio between two things. If one object weighs
one-half as much as another, the ratio between their two
weights is 1:2 (read "1 to 2"). This ration 1:2 may also be

1

written as the fraction — .

2

b. Ratio is also used when speaking of distance tra-

3

veiled. If one says that he has gone — ■ of the way from A to

4

B, the ratio of the distance he has come to the total distance
is 3 :4. The ratio of the distance he has come to the remaining
distance is 3:1.

12. Fractional Equations.— a. Map reading often involves
simple fractional equations in which the value of an unknown
can be found by applying certain simple rules. For example

X 2

(solving for the unknown "X") : — = — .

3 5

To solve for X it is necessary merely to use the same
principles discussed in paragraph 10b, i.e., complex fractions.

X 2

3 5

then

2
5

2
5

X 5

2 5

3 2

5 2

5X XT

6 "-KT

= 1

III A— 9

= 6 (1)

5X = 6

XX

6

6

X = -

—

X

5

5

In solving for X by the method shown above we have,
in effect, cross-multiplied. The procedure of cross-multiplica-
tion is as follows: Multiply the numerator of each side of
the equation by the denominator of the other side of the
equation. Set these two products equal to each other and solve
for the unknown (X).

For example:

3^5
5X = 6
^X 6

X

13. Decimals. — a. Decimals are a means of writing frac-
tions without using the fraction sign ( — ) . Any fraction may
be reduced to decimal form by direct division of the numerator
by the denominator, e.g.

1

4
5

= 4 ) 1.00 =

= .25

2

= 2) 5.0 =

= 2.5

b. Decimals are added and subtracted just as are whole
numbers, except that the decimal point must be placed directly
under all decimal points above it, e.g.

Ill A— 10

2.56

.004
66.
+ .01 +
68.574

21.01
100.0761
.32
9.
130.4061

Subtraction

69.000 .706

— 7.001 -.032

61.999 .674

c. Multiplication of decimals is performed just as
though there were no decimal point present. Then the answer
is pointed off a number of places (starting at the right and
counting left) equal to the total number of decimal places in
the two numbers being multiplied together, e.g.

16.009 (three decimal places)

4.12 (two decimal places)
32018
16009
64036

65.95708 (3 + 2 = 5 decimal places)

6.012 (three decimal places)
12 (no decimal places)

12024
6012

72.144 (3 + = 3 decimal places)

d. Before division can be performed on decimals, the
decimal in the divisor must be moved entirely to the right
hand side of that number, thus

2.25.) 45.00.

The decimal in the dividend must be moved to the right
the same number of places (as shown above — in some cases
zeros must be added on the right of the number). This moving
of the decimal really amounts to multiplying both numbers by
some multiple of ten (in the above case by 100).

After moving the decimal, ordinary division is per-
formed :

20.
2.25.)45.00.

^ 45 r

00

III A— 11

.00002

71.2.). 0.01424

~ ^ 1424

The decimal in the answer is placed directly above the
decimal in the dividend.

Other Examples:
359.4
.006.) 2.156.4
"~" 1_8_
35
30
56

54.

24

24

14. Parallel Lines. — Parallel lines play a large part in map
reading. Since both the geographic and military grid systems
of coordinates (means of location) are based on the properties
of parallel lines, certain of these properties should be under-
stood :

a. Parallel lines are lines in the same plane (two di-
mensional surface) which will never intersect. Thus the
shortest (or perpendicular) distance between parallels is con-
stant.

b. Angles formed by the intersection of a line with a
series of parallels have certain definite relationships:

In figure 2, we have the parallel lines ab, cd, and ef , and
xy is any straight line cutting these parallel lines.

Z_C=Z..E';Z_D = z_F;z_G = ZJ; i lH = .z.K

RD 3503

/ /

Y

A

L/ >

y ;

Figure 2. — Angles formed by a line intersecting parallel lines.

(2) The alternate exterior angles are equal.

LA = LG; LB = LH; LF = LM;LF = LL

(3) The corresponding angles are equal.
LB = LF = LK; LA = LF = LI
LC = LG = LL;LV = LH = zl M

III A— 12

15. The Circle and Its Uses. — a. Since the circle is one of
the most important geometric figures in map reading, its com-
ponent parts and their nomenclature and relationship must
be understood.

Figure 3.— The Circle.

b. In the above figure, point A is the center of the
circle. The line AB is the radius (r) of the circle, or the dis-
tance from the center to any point on the circle. The line BAG
is the diameter (d) of the circle and is equal to two radii
(d = 2r).

If the center A remains in place and the radius AB
swings in a clockwise direction (the direction in which the
hands of a clock move) about A, then the point B will trace
the rim or circumference BECD of the circle. It has been
found bv measurement that the circumference (C) is equal
to Trd. Or = 3.14+)

C = 7rd

since d =

= 2r

then C =

= 27rr

>

III A— 13

c. The circumference is a linear measure and, as has
been shown, is dependent on the length of the radius. A circle
can also be measured by angular units. The unit of angular
measure is the degree, which is independent of the length of
the radius. By definition: Any circle = 360°

1° (degree) == 60' (minutes)
1/ (minute) — 60" (seconds)

d. Whenever two lines intersect at a point an angle
{L) is formed. To measure the angle it is assumed that the
angle is a segment c^ a circle and its measurement is expressed
in degrees. In military map reading this measurement is al-
ways made in a clockwise direction.

For example : In Figure 3, line BA and EA intersect at
A. This forms the angle BAE (XBAE). The angular mea-
surement from BA to EA is shown as 90°. (A 90° angle is
known as a right angle.)

In the same figure, the angle between BA and DA would
be 270°, since angles are always measured in a clockwise direc-
tion on military maps.

e. In Figure 3, the segment of the circumference cut
off by the L BAE is called the arc BE (BE). The straight
line BE is the chord (BE) of the arc BE. As the size of the
angle decreases, the length of the chord approaches the length
of the arc so that for very small angles the length of both is
practically the same.

f. For military use another unit of angular measure
besides the degree is often used because of its simplicity. It
is very important in all phases of gunnery and as gunnery and
understood. This unit is the mil.

A true mil is the angle formed by two radii 1000 units
long and an arc of 1 unit or as it is generally stated: the
angle subtended by an arc of 1 unit and a radius of 1000 units.
In this case one might say that an object one yard long and
1000 yards away from an observer forms an angle of 1 mil at
his eve.

Figure 4. — Diagram of 1 Mil.
Ill A— 14

A circle is arbitrarily assumed to contain 6400 mils
(this circular or military mil is slightly smaller than a true
mil, but the difference is so small that for all practical pur-
poses they are considered to be identical).

An angle measured is mils is measured in a clockwise
direction, just as is an angle measured in degrees.

. 16. Working Problems. — a. Most errors in solving prob-
lems result from carelessness on the part of the student. Such
errors may have consequences that are serious and far reach-
ing. They cannot be tolerated. Large errors, such as mis-
placing the decimal point, seem to be more common than small
ones. To avoid errors, check your results. There is usually
time for at least a rough check. Going back over the work step
by step does not give a satisfactory check. It is better to use
a different method, an independent one if possible.

b. The student must also remember to reduce all dis-
tances or quantities in each problem to the same unit. For
instance, mils and degrees cannot be added together without
first converting one of the two quantities to the other type of
unit.

17. Navy Time. — The Navy and Marine Corps use the Con-
tinental or 24 hour clock system of time. This eliminates the
confusion of a.m. and p.m., morning and evening. The time
is always expressed as a 4-figured number from 0001 to 2400.
Midnight is 2400, high noon 1200. The first two digits are
the hours and run from 00 to 24. The second two digits are
the minutes and run from 00 to 60.

To convert civilian time to Navy time :

a. If a.m. (morning) and before 10 o'clock, prefix a
zero to the hours and minutes to give a 4-figured number;
e.g., 7:45 a.m. becomes 0745.

b. If p.m. (afternoon) add 1200 to the hours and min-
utes; e.g., 4:15 p.m. becomes 1615.

No colons, symbols or breaks of any kind are used to
separate the hours from the minutes.

When adding or subtracting Navy time it is well to
separate the hours and minutes slightly.

Example: A column of troops left the barracks at
0900, marched for 2 hours and 45 minutes, had an hour for
chow, then marched for 3 hours and 30 minutes. At what
time did they reach their destination?
09 00 Time of departure

2 45 First marching period
1 00 . Chow time

3 30 Second marching period
15~75 Total

The above figure indicates 15 hours and 75 minutes total
time.

Ill A— 14(a)

Since 75 minutes equals 1 hour and fifteen minutes, the
time of arrival is 1615.

15 00
1 15

16 15 = Time of arrival.

NOTE: No matter how small the fraction of a minute may be, in
computing time it becomes the next larger whole minute;
e.g., 1614 1/10 or 1614.1 becomes 1615.

18. Table of Equivalents.—

Linear Measure :

1 foot (0 =12 inches (")•

1 yard = 3 feet == 36 inches.

1 statute mile = 1,760 yards = 5,280 feet = 63,360

inches.
1 meter = 1.094 yards = 39.37 inches.
1 kilometer ±= 1,000 meters = 1,094 yards = .62 miles.
1 mile = 1.61 kilometers.

Angular Measure:

360 degrees (°) = 1 circle — 6400 mils.

1° = 17.8 mils.

1 mil = .056°.

1° = 60 minutes (').

V = 60 seconds (").

Geographic or Nautical Measure :

1 nautical mile = 6080.20 feet = 1.1516 statute miles.
60 nautical miles = 1 degree (°) at the equator.
1 knot = 1 nautical mile per hour.
1 fathom = 6 feet (depth of sea).

Surveyor's Measure:

1 link (li.) = 7.92 inches.
100 links = 1 chain (ch.) = 66 feet.
10 chains = 1 furlong = 660 feet.
80 chains = 1 mile.

(The engineer's chain is 100 feet long with links 1 foot
long.)

Ill A— 14(b)

SECTION 3

CONVENTIONAL SIGNS AND MILITARY SYMBOLS

19. Conventional Signs. — a. Map makers have devised a
common set of signs which to the map reader have a definite
meaning. For instance, there are signs for a house, for a
road, for a bridge, etc. These are called conventional signs.
Some of them look enough like the object they are intended
to represent to be easily recognized such as conventional signs
for lakes or bridges. The meanings of some are not so obvious
and must be learned just as new words are learned. Complete
lists of conventional signs authorized for use on military maps
are published in FM 21-30. The most commonly used con-
ventional signs are shown in Figures 5a & 5b and also on the
"Sheet of Standard Symbols". These need not be memorized,
but the student should study them from time to time until
familiar with the forms.

b. Conventional signs vary in size with the scale of
maps. On small scale maps comparatively few objects can
be shown and the signs are reduced to their most elementary
form. As the scale is increased more objects can be repre-
sented.

c. Locations of some objects are shown with more
accuracy than others due to manner in which the topographer
and map draftsman work. Some of these in order of ac-
curacy are:

(1) Triangulation stations.

(2) Surveying monuments.

(4) Important bridges.

(6) Isolated buildings on main roads, Including
churches and schoolhouses.

(8) Streams, contours, and woodlands, cleared
areas, etc. In choosing landmarks for determining location,
these relative values should be kept in mind.

d. When colors are used for War Department maps,
they are used as follows: black for works of man and for
grid lines ; brown for contours, cuts, and fills ; blue for water ;
green for woods and vegetation; red to indicate road condi-
tions.

e. Occasionally conventional signs will be found that
are not given in FM 21-30, but these should be indicated in the
margin of the map with such explanatory notes as are neces-
sary.

Ill A— 15

COMMON CONVENTIONAL SIGNS

Roads, Unimproved - — — — — :

Trails, Good

Trails, Poor Pack or Foot

Railroads (single track) — _ -h — i — i — i — i — i — i — i — i —

Railroads (double track) I 1 1 I I ! I I 1

or

( II II I I I I II ll II H ll )

Bridges (general) .. ) (

Telegraph or Telephone Line T T T T T T T

Power Transmission Line - -•- — ♦____... —

Buildings in General ; ■ WM a &Zl

Church or Place of Worship 6 it

Schoolhouse £ S

it 1

Cemetery = lJJ

Fort ^

Fences (stone)

Fences (worm)

_ / . x Smooth Barbed

Fences (wire) _o — o — o — o x- — x — x — x

Triangulation Station A

Bench Mark (and elevation) . BM X 172

Combined Triangulation Station and

Bench Mark (with elevation) . BM A 172

Figure 5a. — Common Conventional Signs.
Ill A— 16

COMMON CONVENTIONAL SIGNS (Continued)

Streams (in general)

Intermittent Streams

Cliffs

Rocky Land

Hilly Terrain, Tops Outlined

Cuts

Fills _

Marsh or Swamp

:/.v.v.v.v.v.v.v/.v.v.v.v.v.y.".v.

— *T„

Woodland (in general) (E VEN GREEN TIN ?)

Land

Rocky Ledges

Reefs

Cultivated Land

Orchard

Banana

Mangrove

Rice Fields

Land

o is & g> & a

or

or

1L 1L

±L _1L

or

Figure 5b. — Common conventional signs.
Ill A— 17

various types of terrain features. Military symbols have
been developed to represent various types of military organi-
zations, activities, and installations. These symbols are used
to indicate size and identity of various units and installations,
type and location of supporting weapons, and necessary lines
and boundaries for an operation. A material saving of time
in giving orders for military operations may be achieved by
using military symbols to outline operations on a map or a
map substitute.

b. The text "Military Symbols and Abbreviations" lists
the standard military symbols authorized for the Marine Corps,
and shows how they are derived.

Ill A— 18

SECTION 4
MAP MEASUREMENTS

21. Scales. — In map reading the scale of the map is a first
consideration. The scale is the relation between measure-
ments on the map and actual distances on the ground. The
scale of a map is expressed in one or more of the following
ways:

a. Words and figures. — Actual equivalents given in
words and figures as 3 inches equal 1 mile means that 3 inches
on the map equals 1 mile on the ground ; 1 inch equals 200 feet
means that 1 inch on the map equals 200 feet on the ground.

b. Representative fraction. — The scale of a map may
be shown as a representative fraction (usually abbreviated to
RF) . This fraction expresses the ratio between a given dis-
tance on a map and the corresponding distance on the ground.

The RF is shown thus: 1:63,360 or go ogA which means

oo,obU

one unit of distance on the map equals 63,360 such units of

distance on the ground. The same kind of units of distance

measured from the map must be applied to distances on the

ground. For instance, in the RF shown above, 1 inch on the

map equals 63,360 inches (or 1 mile) on the ground

and 1 foot on the map equals 63,360 feet (or 12 miles)

on the ground. The greater the denominator the smaller

the scale; a 1:20,000 map is a large-scale map, and a 1:1,000,-

000 is a small-scale map.

c. Graphic scales. — The figure resembling a small ruler
printed on the map is also called a scale. It is divided into
parts, each division being marked not with its actual length
but with the distance each length represents on the ground.
Usually there will be one part graduated into mile units and
fractions of a mile. The other part is graduated in yards
for more exact measurements of ranges, frontages, and depths.
Many maps also show the kilometer scale. Each graphic scale
consists of a primary scale to the right of zero, and an exten-
sion to the left of zero. The extension consists of one primary
unit of the graphic scale subdivided into appropriate fractions.
Typical graphical scales as used on American maps can be seen
on the lower margin of Figure 6. The scale in Figure 6 has
1,000-yard units for the primary scale and ten 100-yard units
for the extension.

22. Distance. — Once the scale of the map is known, dis-
tances on the ground which are represented on the map can be
determined. Even though the scale is given in words and
figures or as an RF, some sort of graphic scale is usually

ill A— 19

necessary. The graphic scale is the most accurate and the
most common means of determining distances from a map.
Some methods of employing the graphic scale follow:

a. To find distance between two points on map. —

(1) Lay the straight edge of a piece of paper or
other material along two points on the map, mark the location
of the two points on the straight edge by using short straight
marks called "ticks" at right angles to the edge of a paper.

(2) Take the marked straightedge and place it be-
low the graphic scale on the margin of the map to determine
the ground distance required. Where the distance is greater
than the length of the graphic scale, apply the primary scale
one or more times until the remainder can be measured as
explained above. Distances between the smallest divisions
of the scale are estimated.

(3) Example. — (a) Problem. — Figure 6 shows a
portion of a 1 :20,000 map. Required, to find actual distance on
the ground between the house at A and the house at B.

Scale 1:20,000

distance-

(strip of paper)

Figure 6. — Using graphic scale to measure distance.

(b) Solution. — Lay the straightedge of a
strip of paper along A and B on the map and make tick marks.
Take the strip of paper and lay its marked edge along the
graphic scale on the margin of the map as shown in Figure
6(2) . The required distance between ticks is read directly from
the scale as 1,000 yards.

Ill A— 20

b. To find distance along irregular line of map. — It is

sometimes necessary to measure the distance along irregular
lines on a map such as a stream or a winding road. There are
several ways to do this, the two most satisfactory being the
"paper strip" and the "transparent paper" methods.

(1) Paper strip method. — (See Figure 7). Take a
straight edged piece of paper, lay it at the starting point of the
curved distance to be followed and make a tick mark across
the map and paper. At every curve in the course make another
tick mark, turn the paper so the edge again lies along the
course in question and register the last tick marks. Continue
this until the distance is completely measured. The final
position of the paper strip is illustrated in Figure 7. The im-
portant thing is to have the tick mark on the paper strip accur-
ately placed and equal to the corresponding tick mark on the
map, so that the true distance is marked off on the paper strip.
The paper strip is then applied to the graphic scale of the
desired unit as in Figure 6(2) and the ground distance is read.

Caution: Graphic scales are generally shown in miles,
yards and kilometers. Care must be exercised in selecting the
proper graphic scale in the unit of measure desired.

(2) Transparent paper method. — By means of a
straightedge and a sharp pencil draw a long straight line gen-
erally down the center of any transparent piece of paper. For a
starting point, draw a straight line (tick) perpendicular to
and near one end of the first line. Lay the paper on the road
with the starting tick over A so that the long line extends
through 1. Place the pencil point at 1 and pivot the paper
until the long line lies along the course 1-2. Place the pencil
point at 2 and pivot the paper as before. Continue until the
long line lies along course 4-b. Mark the position of B by a
tick on the long line. Measure the distance along the graphic
scale as described above.

23. Time. — a. Conversion of march time to distance, —

It will often be necessary to determine the distance a column
can march in a given period of time. The distance is the
product of the time in hours multiplied by the hourly rate of
march. For example, a motorized unit averaging 30 miles
per hour can cover 4 X 30 = 120 miles in 4 hours. This whole
distance is plotted on the edge of a strip of paper by means of
the mile graphic scale. Then the distance may be laid off
along the straight portions of the road by marking ticks for
each change of direction along the measured portion of the
strip of paper, reversing the methods shown in paragraph 22.
Thus the position of the head of the column at the end of any
given time may be determined.

The Humphrey Time and Space Scale is devised for
rapid computation of rates of march from 1% to 15 miles
per hour.

Ill A— 21

Figure 7. — Measuring distance along a winding road.

b. Conversion of distance to march time. — To deter-
mine how long it will take to move troops from one point to
another, the distance between the two points is taken as above
from any suitable map. The distance divided by the hourly
rate of march gives the time required to move the troops. The
habitual daytime rate of march for foot troops, making allow-
ance for customary halts, averages 2V2 miles per hour. For
example, the time to march foot troops a distance found to be
15 miles on the map is 15 divided by 2.5, or 6 hours.

24. Relation between Distances and Areas on Maps of Dif-
ferent Scales. — Figure 8 shows at a reduced scale an identical
area of ground represented on maps of three different scales;
that is, 1:5,000, 1:10,000, and 1:20,000. A, B, C, and D are
points on the ground. A' B' on a map of scale 1 : 5,000 is just
twice as long as AB on a map of scale 1:10,000. The area
of the map A' B' C D' at scale 1 :5,000 is just four times the
size of the same area at scale 1:10,000. Conversely, A" B" on
a map of scale 1:20,000 is just one-half as long as AB on a
map of scale 1 : 10,000 and the area A" B" C" D" is one-fourth
the size of ABCD. These relationships may be stated as fol-
lows:

a. Distances. — Distances on different maps vary di-
rectly as the representative fractions of the maps and
inversely as the denominators of their respective fractions,
thus (Figure 8) :

1

AB

RF

A' B' R'F'

10,000

5,000

5,000

10,000

III A— 22

RF 1=5,000

Figure 8. — Relation between distances and areas on maps of different
scale. (Scales of maps shown above have been reduced
in printing.)

Ill A— 23

b. Areas. — Areas on different maps vary directly as
the squares of the representative fractions of the maps and
inversely as the squares of the denominators of their respec-
tive fractions, thus (Figure 8) :

1 ^ 2

ABCD
A'B'C'D'

(RF)
(RF')

10,000J ( 5,000 ) 2 1
2 ~ (10,000 ) 2 ~~ 4

5,000

25. Determination of Scale of Map and Construction of
Graphic Scale. — It is important that the user of a map be able
to determine the RF of a map when in the field and readily
construct a suitable graphic scale for use in the event that
the scale data are missing from the map. The procedure is
as follows:

a. Determination of scale. — The scale of a map may
be determined from known distance on the ground, or from
scaled distance on another map of known scale.

(1) By measurement of distance between two
points on ground. — (a) Locate two objects on the ground
which can be identified on the map, such as bridges, houses,
etc.

(b) Estimate, stride, or measure on the
ground in some manner, the distance between the selected
points, and convert into inches. (The method of measuring
should depend on accuracy required, time available, etc.)

(c) Measure in inches the distance on the
map between the two points selected.

(d) Determine the scale from the relation —

/-op distance on map in inches \

V distance on ground in inches /

RF =

GD V distance on ground in inches

This expression, when reduced to a fraction the nume
rator of which is unity, becomes

1 /«■„ l

RF

GD
MD

(

RF

distance on ground in inches
distance on map in inches

5

NOTE: Distances may be expressed in any unit of measurement pro-
vided the same is used for both map and ground distances.
Example: Map distance between two points = 3 inches;
ground distance between corresponding points = 5,208.3
yards.

1 1
RF = =

/ 5,208.3 X 36 inches \
\ 3 inches /

62,500

III A— 24

(2) By measurement between two points on map
of known scale. — (a) Locate two objects on map of known
scale which can be identified on the map the scale of which is
to be determined.

(b) Scale from both maps the distances be-
tween the points in the same unit of measurement (inches).

(c) Determine the scale of the map by one
of the two methods given below:

1. Convert distance on map of known
scale to distance on the ground, and solve as in (1) above, or

2. Determine scale from the relation —

RF of the map _ distance on the map

RF of map of known scale distance on the map of known scale

Example: Distance between two points on the map of unknown
scale = 8 inches.

Distance between corresponding points on a map of 1:20,000
scale = 4 inches.

RF 8

20,000

8
RF = — x

4 20,000 |4| 10,000

20,000 X

8

It is seen from the above that the denominator of
the RF of the map (10,000) is obtained by multiplying the
denominator of the RF of the map of known scale (20,000)
by the distance measured on the map (4) and dividing by the
distance measured on the map the scale of which is sought
(8).

b. To construct a graphic scale (Figure 9a). — "(1) Sup-
pose it is desired to construct a graphic scale to read 1,000
yards for use on a map with an RF of 1 : 10,000. The first step
is to find the total length of the scale by application of the

formula RF = ™-

MD = map distance = total length of scale in inches.
GD = ground distance = 1,000 yards = 36,000 inches.
RF = 1:10,000.

1 MP

10,000 — 36,000

10,000 MD = 36,000.

MD = 3.60 inches (total length of scale
representing 1,000 yards to an RF of
1:10,000.)

Ill A— 25

The next step is to lay off a line the total length of the
graphic scale and then subdivide it into the desired number of
divisions. In this case it is desirable to divide the scale into
100 yard divisions, with the leftmost 100 yard division again
subdivided to 20 yard divisions to form an extension or second-
ary scale. If the total length of the scale was such that it was
conveniently divisible by the use of a ruler, we would divide it
in that way, (for example, if the total length was 5 inches,
each 100 yard division would naturally be .5 or y% inch long
which is easily measured) but if the total length is not easily
divisible as in the case of 3.60 inches a geometric means of
division is used.

(2) Geometric division of a line. — (a) Line ab
(Figure 9a) is 3.60 inches long. We wish to divide it into 10
equal parts.

(b) Draw a line from a at an acute angle
from line ab. This is line ab'. The length of ab' should be such
that it is easily divisible into the total desired number of di-
visions. In this case 10 divisions are desired so a 3-inch line
is drawn. With an engineer's scale this can be divided into
10 divisions .3 inch long.

(c) Connect b and b' with a construction line

(linebb').

(d) Draw parallels to bb' from ab' to ab.
These parallels will divide ab into 10 equal parts.

(e) The extension at the left of the scale can
be further divided in the same manner.

(If the method of constructing parallels is not under-
stood see Figure 9b. A right angle and a straight edge are the
tools required. The engineer's scale and military protractor
are the most convenient.)

(a) Lay the rectangle so it connects bb'.

(b) Place the straight edge along the upper
edge of the rectangle (xy) .

(c) Holding the straight edge fast, slide the
rectangle to point 9 and draw de ; de will be parallel to bb'.

(d) Continue until ab is totally divided.

(3) Another method not so accurate as the above
but simpler and quite satisfactory for practical purposes is
to compute the length of one 100-yard graduation (or any-
other suitable division) of the primary scale and then apply
that as many times as necessary along a line. For exam-
ple, in the case of the map whose RF was deter-
mined as 1 :2,769, the length of a 100-yard interval of the

O CLC\C\

scale would be ? fi r - = 1.3 inches, approximately. Point off

this distance as many times as 100-yard graduations are
required for the primary scale, subdividing the left interval
as the extension.

Ill A— 26

/y\

y<X^\

f <^N \ ^ •

^^ X N \ \
y^yK \ \ \ . \ \ \

>< \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \

\y \

QHHH

1— — 1 ^— 1 — 1— 1 lb

'OoHi j°

1 2 3 4 5 6 8 900 yds

3 60" >'

RF=l:iO,000

Figure 9a

/ * y^\

X^y\ \

/ ■<\$■ / \ \

X *•■ / \ \t'

y^ 2r\

S \ * / X \

X \ 1 ^^ \ \

/ x \ >r \ \

* \ \v^ \ \

\ <b >o \ \

*>c\ \ \

>r x \ \ \ .

V^ \ \ . \ . \

v^ \ \ \ \

\ y

\ \ \ \

/^

\ \ \e \ b

u

\ \ X \

\ \ \ y

\ \ X

\ \ /

\ \ x

Figure 9b \ \ /

\ \/

\ /

\y

RO 3503-1

Figures 9a & 9b. — Construction of graphic scales.

Ill A— 27

26. Time-Distance Scales. — In solving tactical problems or
in planning military operations on maps, time-distance scales
frequently prove time-saving devices of great usefulness. A
time-distance scale is a scale whose graduations are time in-
tervals of distance to the scale of the map at a given rate of
movement (fig. 10). Suppose that a time-distance scale gradu-
ated in hours and minutes of time at a given marching rate,
is desired for use on a topographic map 1 :62,500. To con-
struct such a scale, the procedure is as follows:

a. (1) In 1 hour, infantry marches 2% miles or
2i/ 2 X 63,360 = 158,400 inches.

158,400

(2) 158,400 inches on the ground == = 2.53

62,500
inches on a map whose scale is 1:62,500.

(3) On a suitable strip of paper along a straight
line ab (Figure 10), lay off as many 1-hour intervals of 2.53
inches each as may be desired in the scale. Subdivide the left
interval on the scale extension into 1-minute, 5-minute (used in
Figure 10), or 10-minute graduations, depending on the least
scale, indicate the RF of the map to which the scale applies
and the marching rate to which constructed.

b. (1) In 1 hour, a motor column marches 30 miles
or 30 X 63,360 = 1,900,800 inches.

1,900,800

(2) 1,900,800 inches on the ground = =

62,500
30.41 inches on the map.

This shows why operations for units with such rates
of march would ordinarily be planned on smaller scale maps.
Hence the time-distance scale for a motor column is shown
in Figure 10 for a 1:500,000 map, making a 1-hour march
equal to 3.80 inches on the map.

Ill A— 28

2.53

AW

X \ \ \ \

X \ \ \ \ \
x \ \ \ \ \ \

x \ \ \ \ \ \ \

< \ ^ \ N ^ \ \ \ \

X \ \ \ \ \ \ \ \ N \ '

X \ \ \ \\ N \ \\ V\!

2.53'

T ) ) i 1 )))))) " \ i

b

ZZ)
IHR

60 MiN

30 20 10

RF 1=62,500 (INF. @ 2 '/2 MPH)
INFANTRY

10

RF l»500,000 (MOTOR @ 30 MPH)
MOTOR COLUMN

Figure 10. — Time — Distance scales.

Ill A— 29

SECTION 5
DIRECTION

27. Need For Direction. — To locate objects, both direction
and distance are needed. For example, an object can be
located by telling how far away and in what direction it is
from a given point. Most persons are familiar with the
established geographic terms, north, south, east, and west.
These are the directions that are indicated by the common
military watch compass.

28. Units of Angular Measure. — a. General. — Angles may
be measured in degrees, minutes, and seconds, or in mils (see
Figure 11). Normally, only persons in artillery or heavy weap-
ons units have to use the mil since their fire control instru-
ments are generally graduated in mils rather than in degrees.
Other personnel usually use degrees, minutes, and seconds.

MILS

6400 100 200

Figure 11. — Units of measurement.

Ill A— 31

b. Angles. — (1) In degrees, minutes, and seconds. —

If the circumference of a circle is divided into 360 equal
parts by lines drawn from the center to the circumference,
the angle at the center between any two adjacent lines is one
degree. There are 60 minutes in a degree, and 60 seconds in
a minute. Thus:

60" (seconds) == V (minute)

60' (minutes) =1° (degree)

360° (degrees) = 1 circle or a circumference.
Angles are written— 137° 45'23".

(2) In Mils. — If the circumference of a circle is
divided into 6400 equal parts by lines from the center to the
circumference, the angle at the center between any two adja-
cent lines is one circular or military mil. A true mil is the
angle subtended by an arc of one unit on a radius of 1000 units.
Therefore, the circular or military mil is slightly smaller than
the true mil, but for all practical purposes they are considered
to be identical. An angle would then be expressed in mils as
1,327 mils.

c. Relation between degrees and mils. — Degrees may
be converted to mils or mils to degrees by using the following
simple conversion factor :

360° = 6,400 mils

1° — ~i^K = 17.8 mils (or 18 mils, approximately)

Hence 10° = 10 X 17.8 = 178 mils (or 180, approxi-

Qftf)

1 mil = wj^ — .056° (or 3.4', approximately)
b4(Ju

Hence 100 mils = 100 X .056 = 5.6° or 5°36'

29. Base Direction. — For military purposes direction from
one point to another is always expressed in terms of an angle
at the initial point between the line joining the points and
some fixed or easily established base direction line. There
are three base directions from which other directions are
commonly measured, namely true north, magnetic north, and
grid north, shown on maps by a star, half arrowhead, and y,
respectively (Figure 12).

a. True north. — The direction to the true north pole.
It is used in surveying and other permanent work where great
accuracy is required. Where meridian lines or longitude lines
are shown on maps they represent true north and south direc-
tion. For ordinary military map reading in the field, true
north will normally be used only as a base from which declina-
tions are computed. It normally is not used as a direction in
marching by compass or orienting a map.

ill A— 32

mately)

b. Magnetic north. — The direction of the north mag-
netic pole. It is indicated by the N (north seeking) end of all
compass needles. It is ordinarily used for field work because
it can be found directly by means of the common compass.

c. Grid north. — The direction of the vertical grid lines
(north-south grid lines) usually found on military maps. On
maps with military grid, determination of directions from grid
north is convenient because grid lines are located at frequent
intervals.

30. Declination. — Declination is the difference in direction
between true north and either magnetic north or grid north.
Hence there are two declinations, magnetic declination and
grid declination or gisement.

a. Magnetic. — Due to the inequality of distribution of
magnetic forces throughout the earth and the fact that these
forces are variable with reference to both time and place,
there will always be, except in very few localities, an angle
between true north and magnetic north. This angle is called
the magnetic declination. Where the compass needle points
east of true north the magnetic declination is easterly and

2°25

6°40'

2°25

9° 05

Approximate Mean Declination 1940 Annual Magnetic Change 3' Increase

Figure 12. — Declination.
Declination is either shown as in (a) as grid declination (gise-
ment) and magnetic declination measured from true north, or as in
(b) as grid declination (gisement), and the total deviation between
grid and magnetic.

Ill A— 33

when the needle points west of true north the magnetic decli-
nation is westerly. In order to record and study the mag-
netic disturbances which cause the compass needle to deviate
from true north, maps have been prepared showing points on
the surface of the earth where magnetic north coincides with
true north. Lines connecting these points are called agonic
lines. Points on these maps having the same magnetic decli-
nation are located and connected by other lines called isogonic
lines. (See Chart Figure 13.)

In the United States, isogonic lines run in a general
north and south direction, but meander within wide limits,
sometimes doubling back on themselves. The magnetic decli-
nation in the United States varies from 25° easterly in the
State of Washington to 22° westerly in the State of Maine.
It is for this reason that precise maps covering and consider-
able area are based on the true meridian or a grid system
referred to true north.

The discussion up to this point covers magnetic decli-
nation as related to place or the location of the observer.
There is also the time factor which introduces an additional
necessary correction. The location of the magnetic pole and
hence the direction of magnetic north changes with the pass-
age of time. This change is computed in annual increments and
is called annual magnetic change and is shown with other
marginal data on maps of the United States published every
5 years by the U.S. Coast and Geodetic Survey. This annual
magnetic change in some localities of the United States may
increase or decrease the magnetic declination as much as 4
minutes annually. Every standard map shows in diagramatic
form the average relation of magnetic north to true north in
the area covered by that particular sheet as of a stated date.
The annual magnetic change and how it is applied as a correc-
tion to increase or decrease the magnetic declination is also
shown as a marginal note. On nautical or coast charts the
annual magnetic change is shown as the annual increase or
decrease in variation and is so noted on the chart near each
compass rose, so that the proper corrections may be computed
and added, if an increase, or subtracted if a decrease from the
magnetic declination indicated on the map as the declination
which was correct only for the year indicated.

The method of computing and applying the annual
magnetic change is illustrated with reference to figure 12b, as
follows :

Magnetic declination in this illustration in 1940, the
date of the map, was 9°5' less 2°25' equals 6°40'.

Annual magnetic change 3' increase.

Total magnetic change accumulated to 1944 equals 03'
X 4 years = 12'.

Magnetic declination 1944 would be 6°40' plus 12' or
6°52'.

Ill A— 34

Figure 13. — Lines of equal magnetic declination and
III A— 35

of equal annual change in the United States for 1935.

b. Grid. — Grid declination is the fixed difference in
direction between true north and grid north. Because of the
fact that the meridians converge to meet at the pole while all
the north-south grid lines (Y lines) of the same grid zone are
parallel to one another (see par. 44 for an explanation of the
military grid system), there is a deviation betwen true north
and grid north except along the central meridian of the grid
zone. This deviation is called grid declination or gisement and
reaches a maximum of 3° at the edge of the grid zone. It
is illustrated in Figure 15 which shows a sketch of the projec-
tion of the earth with abed representing the area of a map on
which the line op is the projection of the central meridian of
the grid zone. The north-south grid lines are straight lines
parallel to op. The projections of all meridians other than op
are curved converging lines which deviate in direction from
the direction of the north-south grid lines. This deviation is
designated as west grid declination for all points west of the
central meridian, as at point m, and as east grid declination
for all points east of the central meridian, as at point s. The

-2°25'

l°30 -

Magnetic North IO e
West of Grid North.

Magnetic North
7° West of Grid

North

Magnetic North 12
East of Grid North

Figure 14. — Determining difference in direction between grid and mag-
netic north.

Ill A— 37

declination is determined by finding the angle that the Y-grid
line makes with true north at the point in question. Although
the grid declination varies at different points on a map, this
variation on the tactical map is so slight that the average
grid declination for the area may be used as the actual grid
declination at any point on the map sheet wi'thout introducing
an appreciable error. Every standard map should show in
diagrammatic form the average grid declination for the area
represented by the map.

31. Use. — Figure 14 illustrates three positions of grid, mag-
netic, and true north. There are other possible positions.
In ordinary map reading the difference in direction between
grid north and magnetic north is desired rather than their
difference from true north. This can be found in the thi.ee
example as follows: in Figure 14 © the difference between
magnetic and grid declination is seen by inspection to be
10°0' (12°25'-2°25'). In © it is 12° 0' (13°30'-1°30'). In
® it is 17°0' (15°0'+2 o 0'). In the other possible positions
of these lines, the declination is determined in a similar man-
ner. When starting to use a map, determine the angle be-
tween magnetic north and grid north as described above.
Write this down on the map and figure all azimuths on this
basis.

32. Azimuth. — In describing the position of one point on a
map or in the field with reference to some other point, we use
a standard system of measuring direction. In military work
the azimuth method has been adopted for the purpose. Mili-
tary azimuths are always measured clockwise from magnetic,
true, or grid north. Thus there are three kinds of azimuth
for any given line: magnetic, true, and grid.

a. Magnetic. — The magnetic azimuth of any given line
is the angle measured clockwise from magnetic north to the
given line (fig. 16).

b. True. — The true azimuth of any given line is the
angle measured clockwise from true north to the given line
(fig. 16).

c. Grid. — The grid azimuth of any given line is the
angle measured clockwise from grid north to the given line
(fig. 16).

d. Back Azimuth. — In reference to Figure 17, assume
CR 47 to Hill 172 and found it to be 100°. You then decide that
you want to know the azimuth from Hill 172 back to CR 47. By
geometry it is known that angle a is equal to angle a' ; that is,
if two parallel lines (the magnetic north lines at CR 47 and
Hill 172 are near enough that they can be assumed to be par-
allel — the convergence is negligible) are cut by a straight line,
corresponding angles are equal angles. Also it is known that
the sum of all angles on one side of a straight line through a

III A— 38

point are equal to 180° ; hence, angle b equals 180°. The azi-
muth from Hill 172 back to CR 47 is angle c, which is the sum
of angles a' and b, or 100° plus 180° equals 280°. This is
the magnetic back azimuth of the line from CR 47 to Hill 172.
Therefore, the back azimuth of a line from you to a given point
is really the azimuth from the given point back to you. In
order to convert forward azimuths to back azimuths :

(1) If the azimuth is less than 180° convert by

(2) If the azimuth is greater than 180° convert
by subtracting 180°.

The same rules apply for converting back azimuths to
forward azimuths.

Just as a line can have three - different forward azi-
muths — true, grid, and magnetic — there are also three back
azimuths for each line. Both forward azimuths and back
azimuths should always be stated as true, grid, or magnetic.

NORTH POLE
(Tru e No rth )

WEST

JEAST

^=L

SOUTH

R.D.3503

Figure 15. — Diagram illustrating reason for grid declination.

Ill A— 39

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RO. 3503

Figure 16. — Example of relationship between three base directions on a
map, showing corresponding azimuths and back azimuths
of line OA.

Ill A— 40

Figure 17. — Back azimuths.

33. Bearing. — a. The new lensatic compass gives direction
by magnetic azimuths. Watch compasses, many of which are
still in use, give directions by bearings. A bearing of a given
line is an angle and direction which the line makes with
respect to a north or south direction line. Bearings are stated
by quadrants (quarters of circles) and never exceed 90°.
Figure 18 shows how bearings are measured and indicates
relationship between bearings and azimuths. Figure 19
illustrates the expression of a typical direction in each quad-
rant both as an azimuth and a bearing.

degrees are identical to the numerals used to express magnetic

Example: N 89° E = 89° magnetic azimuth.

bearings are converted to azimuths by subtracting from 180.

Example: S 10° E = 170° magnetic azimuth.

bearings are converted to azimuths by adding 180.

Example: S 29° W = 209° magnetic azimuth.

bearings are converted to azimuths by subtracting from 360.

Example: N 15° W = 345° magnetic azimuth,

III A— 41

N ° W

AZIMUTH = 360°-BEARING
BEARING = 360°-AZIMUTH

W-90°

AZIMUTH= 180°+ BEARING
BEARING=AZIMUTH-I80°

AZIMUTH =BEARING
BEARING=AZIMUTH

90°-E

AZIMUTH = I80-BEARING
BEARING = I80£AZIMUTH

ARROWS INDICATE THE DIRECTION OF MEASURMENT OF THE BEARINGS IN EACH QUADRANT FROM 0°T0 90°
AZIMUTHS ARE MEASURED IN A CLOCKWISE DIRECTION FROM 0° ( NORTH POINT) TO 360°

Figure 18. — Diagram indicating relation between bearing and azimuth.

34. Local Magnetic Attraction. — In addition to the compass
variation caused by magnetic declination, the magnetic com-
pass is affected by the presence of iron and electrical fields of
magnetism. Consequently, great care should be taken not
to approach such local magnetic attraction within a dis-
tance which will cause the magnetized compass needle to
deviate while making observations to determine direction.
The rifle, pistol, and helmet must be laid aside when reading
the compass. The following are the minimum safe distances
for visible masses of iron and electrical fields of magnetism :

Yards

High tension power lines 150

Heavy gun 60

Field gun and telegraph wires 40

Barbed wire 10

III A— 42

BEARING N40°W

AZIMUTH 320°

BEARING N45°E
AZIMUTH 45°

BEARING S 75° E

AZIMUTH 210°
BEARING S 30° W

RD 3503

Figure 19. — Typical direction expressed as azimuth and as bearing.

35. Determination of Direction by Field Expedients. — a.
By aid of watch and sun. — North can be determined with an
error of less than 8° if the sun is visible and a watch showing
approximately the correct sun time is available. Point the
hour hand, watch held face up, at the sun. This is facilitated
by casting the shadow of a vertical pencil across the face of
the watch and by then bringing the hour hand into this
shadow. A line drawn from the center of the dial to a point
halfway on the smaller arc between the hour hand and the
12 of the watch will point south. In the Southern Hemis-
phere the watch must be held face down and this line will
point north. This method is difficult to use when the sun is
very high in the heavens and is of little or no use in the Trop-
ics.

Ill A— 43

b. By rising and setting of celestial body. — Observe
the magnetic azimuth of the sun, a planet, or a bright star at
rising and setting on the same day or at setting on one day
and rising the next. Add these two azimuths together. Take
the difference between this sum and 360°. One-half of this
difference is the declination of your compass — east, if the
sum of the azimuths is less than 360° ; west, if it is greater.
In using this method the observations are best taken when the
object is just above the true horizon, or at a gradient of zero.
This can usually be done if a high point is chosen for observa-
tion. If this cannot be done, be careful to take both observa-
tions with the object at the same gradient, as determined with
a clinometer. This is most important with the sun. Under
the least favorable conditions an inequality of 1° in the gradi-
ents at the time of observation on the sun may introduce an
error of V2 in the result. In using a star, choose one which
rises nearly east from the point of observation. If this is
done the inequality of a degree in the gradients will be im-
material. Both observations need not be made at the same
point, but should not be more than 10 miles apart in east and
west or north and south directions.

c. By aid of sun and plumb line. — On a level piece of
ground, lean a pole toward the north and rest it in a crotch
made by two sticks. Suspend a weight from the end of the
pole so that it nearly touches the ground ; then, about an hour
before noon, attach a string to a peg driven directly under the
weight and, with a sharpened stick attached to the other end
of the string, describe an arc with a radius equal to the dis-
tance from the peg to the shadow of the tip of the pole. Drive
a peg on the arc where the shadow of the tip of the pole rested.
About an hour after noon, watch the shadow of the tip as it
approaches the eastern side of the arc and drive another peg
where it crosses. By means of a tape or string, find the mid-
dle point of the straight line joining the last two pegs men-
tioned. A straight line joining this middle point and the peg
under the weight will, for all practical purposes, be true
north.

d. By means of North Star (Polaris). — Ursa Major
(Big Dipper) is the easiest constellation to distinguish and
provides the best means for locating the North Star. The
two "pointers," or the stars forming the lip of the dipper,
point to the North Star (Polaris) at all times as the Dipper
appears to circle the pole. On the opposite side of Polaris
and at about the same distance from it is the constellation of
Cassiopeia. Its form is that of the letter "W." The great
importance which attaches to the North Star is that it revol-
ves about the celestial North Pole in a small circle whose
radius is slightly more than 1°. It therefore appears to the

III A— 44

eye to be always in the same place. An observation of the
North Star to determine true north, when the Dipper and Cas-
siopeia are above and below the North Star, will give the
declination of the compass to within the least reading of the
compass.

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RD 3503

RECTANGULAR

Figure 20. — Military protractors.

36. Protractor. — Angles of azimuth or bearing are measured
or laid off on a map by means of an instrument called a pro-
tractor. Figure 20 illustrates two types ; the semicircular type
is the more common. Each represents one half of an azimuth
circle. In the figure it will be noted that two scales are shown,
one reading from 0° to 180° and one from 180° to 360°, used
for reading azimuths greater than 180°.

Ill A— 45

736

735

Line extended
to facilitate

RD 3503

Figure 21. — Using protractor to measure map azimuth.

37. Use of Protractor. — a. To measure azimuth of any line

on map (Figure 21. ) . — (1) Required, to find the grid azimuth
of the line from the CR (crossroads) at A to the house at B.
Extend the line AB until it intersects the 349 grid line. Lay
a protractor on the map with its center at this intersection
and the straight portion lying along the 349 grid line. Read
the grid azimuth of AB. This azimuth is seen to be 137°.

(2) Required, to find the grid azimuth of the
line from the CR at C to house at D. Extend the line CD a
sufficient distance so that it will extend beyond the edge of
the protractor. Lay the protractor on the map with its center
at the intersection of CD with the 351 grid line and the
straight portion lying along the 351 grid line. Since the azi-
muth of the line is greater than 180°, the scale reading from
180° to 360° will be used to determine the azimuth of CD.
This azimuth is 226°.

Ill A— 4G

736

constructed parallel to Y grids

Point from
which 75°
azimuth is
to be plotted.

735-

350 351 352

Azimuth of 75° plotted from crossroads 685.

Figure 22. — Plotting azimuths.

b. To plot on map line with given azimuth (fig. 22.). —
Required, to plot from CR (crossroads) 685 a line with a
grid azimuth of 75°. Construct a line through the CR paral-
lel to the north-south grid. Lay a protractor on the map with
its base on the line and its center at the CR. Plot the point
P at the 75° reading on the outer scale of the protractor. Re-
move the protractor and draw a line from the CR through P.

38. Locating Point by Intersection and Resection. — a.
General. — Sometimes it will be necessary for patrol leaders or
other military personnel to determine map position of points
or objects located either in enemy or other inaccessible terri-
tory. Also it may be necessary to find their own map posi-
tion from inaccessible but visible points that are shown on
the map. Figure 23 shows how both these operations can be
accomplished.

Ill A— 47

736

735

352

Where azimuths from road junctions to gun are known, their plotting
gives location of the gun. Where azimuths from gun to road junctions
are known, they can be converted to back azimuth and gun position
plotted as before.

Figure 23. — Location by intersection and resection.

b. Intersection. — -Required, to find map position of an
enemy gun that has been spotted at the point P (Figure 23) on
the ground. Both CR 685 and RJ 573 are in our territory and
the enemy gun is visible from both of these points. By means
of a prismatic compass, the magnetic azimuth was taken from
CR 685 to the gun at P. Converted to grid azimuth, it was 37°.
This grid azimuth was then plotted from CR 685 as shown.
Likewise, the magnetic azimuth from RJ 573 to P was taken
and converted to grid azimuth. The grid azimuth was 327°.
This azimuth was then plotted from RJ 573. The intersection
of these plotted azimuths gives the map position of the gun at
P which can be checked by additional similar observations.
Observation points should be selected such that the plotted
azimuths cross at as near a 90° angle as possible so that the
point of intersection is definite.

c. Resection (Figure 23).- — (1) Required, by someone
at P, to find map positions of gun at P. This gun is in our terri-
tory but no landmarks or other easily identified terrain fea-
tures are close enough to permit location from these points.
However, CR 685 and RJ 573 are visible from P and are also
shown on the map. The azimuths from P are read to both

III A— 48

road intersections. These azimuths are then converted to
grid back azimuths and plotted as before, giving the map
position of the gun.

(2) Note that in using these two systems no
measurement of distance is required. Location of position is
determined merely by reading two angles and plotting two
lines.

Ill A— 49

i

SECTION 6

COORDINATES

39. General. — In military operations it is frequently neces-
sary to refer to points on the ground or terrain features in
short, convenient, unmistakable terms. The easiest way to
accomplish this is to designate the point when given on a
map by its name or number. Military maps often show names
or numbers of all important locally known features. Hills,
usually in terms of their elevation in feet above sea level, thus
serving the dual purpose of designating the feature and also
giving its elevation. But it is not possible to number or
name all features of military value on a map. Also it is
often difficult to find such points on the map even when they
are named or numbered. Thus some simple method or sys-
tem for describing the position of a point or a place on a
map is essential for quick and accurate identification. The
use of coordinates has been adopted to serve this purpose.
Systems of Coordinates. — a. In order to express abso-
lute or relative positions of points, either on a map or on the
terrain, one or more of the several different systems of coordi-
nates may be selected. Each system has its appropriate uses.
The names of the systems in most common use are :

(1) Polar coordinates.

(2) Rectangular coordinates.

(3) Geographic coordinates.

(4) Grid coordinates.

(5) Thrust line coordinates.

b. Rectangular and polar coordinates are classified as
relative coordinates because they are determined by reference
to a base point (and direction) local to some map and. selected
by some individual. Since an indefinite number of persons may
be using a map of the same area, but perhaps using different
base points, a given point on the map could therefore have an
indefinite number of polar or rectangular coordinates assigned
to it.

Geographic and grid coordinates are termed absolute
coordinates because each is determined by reference to a per-
manently fixed base point and direction which have been offi-
cially adopted for that purpose. Thus only one set of geo-
graphic coordinates or, for any grid zone, only one set of grid
coordinates can be assigned any point and this set of coordin-
ates is not affected by the selection of map.

Thrust line coordinates are neither absolute nor relative
but combine some of the features of both types, because they
are measured from a temporarily fixed base point and a tem-
porarily established base direction so that for only a limited
period of tim° are the coordinates absolute.

Ill A— 51

40. Polar Coordinates. — Polar coordinates are used in desig-
nating points located with a compass in the field and in
designating positions on maps not equipped with the military
grid. They consist of an angle from a known base direction
and a distance from a known base position. The base position
is the origin of coordinates. It may be a fixed landmark,
a survey monument, or any other position easily identified on
the map and on the ground. The base direction may be true,
magnetic, or grid north or south. The angle may be expressed
as azimuth or bearing, the distance in any convenient distance
unit. The base position or origin should be fully described.

Example: Battle map, Fort Belvoir, 1:20,000 (1935),
BM 38, Accotink (village), distance 500 yards N.30°W.
magnetic.

1792

1791

1790

1365

1366

1367

Figure 24.— Polar coordinates: BM 38. Accotink (village), distance
1,800 yards on grid azimuth 22° 30'.

NOTE: Figures 24 and 25 refer to the Fort Belvoir map because it
is issued with this text. Polar and Rectangular coordinates
are used chiefly on ungridded maps, but may be plotted on
gridded maps.

Ill A— 52

Battle map, Fort Belvoir, 1:20,000 (1935), BM 38,
Accotink (village), distance 1,800 yards, on grid azimuth
22° 30'. The point so designated is marked b in figure 24.
The base position, BM 38, is marked a, the distance from the
base position is the line ab, the base direction (grid north) is
ay, and the angle from the base direction is yab.

In dealing locally with many points common to a
single map sheet, the sheet reference may be omitted.

a. To plot position of point, polar coordinates of which
are given. — (1) Locate on the map the landmark or other
base position (origin) given.

(2) Through the base position draw a guide line
parallel to the base direction.

(3) With a protractor, point off from the guide
or bearing).

(4) Through the point thus established and the
base position (origin) draw a guide line.

(5) Along this guide line from the base position
lay off the given distance to scale.

b. To determine polar coordinates of map position with
respect to given position and given direction. — (1) Locate
on the map the given base position and through it draw a
guide line parallel to the base direction.

(2) Draw another guide line through the base
position and the point whose polar coordinates are sought.

(3) With the protractor, measure the angle (azi-
muth or bearing) which the direction line established in (2)
above makes with the base direction line established in (1)
above.

(4) With a suitable scale at the RF of the map,
measure the distance from the base position to the point the
coordinates of which are sought.

41. Rectangular Coordinates. — Rectangular coordinates are
used in designating points on ungridded maps without the
aid of a protractor. They consist of two distances measured
at right angles from a base position. The base position
(origin) should be a landmark, survey monument, or other
well-established position. The base position, distances, and
directions should be fully stated, thus:

Battle map, Fort Belvoir, 1:20,000 (1935), BM 38,
Accotink (village), 1,500 yards east (magnetic), 1,100 yards
north (magnetic) . The point so designated is marked c in Fig-
ure 25. The base position, BM 38, is marked a, the base direc-
tion (magnetic north) is am, the direction of the line ab (grid
east) makes a right angle with the line am, and the respective
distances are ab and ac.

Ill A— 53

1792

1791

1790

1365

1366

1367

R.D. 3503

Figure 25. — Rectangular coordinates: BM 38, Accotink (village), 1,500
yards east magnetic, 1,100 yards north magnetic.

a. To plot map position, rectangular coordinates of
which are given. — (1) Locate on the map the base position
(origin) given.

(2) Through the base position draw a guide line
parallel to the base direction.

(3) Through the base position draw a guide line
at right angles to the base direction.

(4) From the base position along these lines point
off to scale the respective distances in the respective direc-
tions as given.

(5) Treat these distances as the adjacent sides
of a rectangle; complete the rectangle (other two sides) with
construction lines. The intersection of these two construction
lines is the point sought.

ill A— 54

b. To determine rectangular coordinates of map posi-
tion with respect to given base position and direction. — (1)

Identify on the map the given point and the given base
position.

(2) Through the base position draw a guide line
parallel to the base direction.

(3) Through the base position draw a guide line
at right angles to the base direction.

(4) Through the given point drop perpendiculars
to the lines established in (2) and (3) above.

(5) From the base position scale the distance
along the guide lines of (2) and (3) above to the respective
perpendiculars. These distances are the rectangular coordi-
nates sought.

42. Scale of Proportional Parts. — Map reading sometimes
requires the measuring or location of a point or line between
parallel lines. If the lines are spaced an equal distance, this
presents no problem, but if they are unequally spaced as in
the case of geographic grid lines a special method of measure-
ment is required. This may be done with any graduated
ruler because of certain properties of parallel lines.

a. In Figure 26, lines AB and CD are parallel and
spaced an unequal distance apart. We wish to find the per-
centage of the total distance point X is from line AB.

b. Select any scale on an engineer's scale that is readily
converted to 100. (An engineer's scale is divided decimally.)
In this case 20 scale was selected; 5 units is a convenient
length and easily converted to 100 by multiplying by 20.

c. Place the scale so the is on line AB and the 5 is on
line CD.

d. With the on line AB and the 5 on line CD, slide
the scale along the parallels until the point X lines along the
scale.

e. The reading of 1.9 is converted to percentage
by multiplying by 20; hence, 1.9x20 = 38% of the total
distance away from AB to CD.

f. If the lines AB and CD were a thousand yards
apart, point X would then be 380 yards from AB.

NOTE: The angle the scale is held to the lines is immaterial as long as
the is held on the base line (in this case AB) and the
other selected number (in this case 5) is held on the other
line.

Ill A— 55

Figure 26. — Measuring between parallels.

g. If the lines AB and CD were part of a geographic
grid and were one minute apart and you wished to find the
number of seconds point X was from line AB, the method
would be modified as follows :

60 seconds = 1 minute

5 X 12 = 60

1.9 X 12 = 22.8 = 23"

(As before 5 units is a
convenient length and in
this case easily converted
to the total of 60 parts by
multiplying by 12.)

Therefore, point X is 23" from AB.

43. Geographic Coordinates. — The system of latitude and
longitude lines projected on a map represents the geographic
or spherical grid covering the earth. In this system the base
position (or origin) is the intersection of the meridian of
Greenwich, known as the prime meridian, with the Equator.
The base direction is true north (or south). Distance on the
spheroid (earth) is reckoned in units of degrees, minutes,
and seconds of latitude up to 90° north or south of the Equator,
and in degrees, minutes, and seconds of longitude up to 180°,
east or west of the prime meridian. The location of any
point on the surface of the earth is denned in terms of the
parallel of latitude and the meridian of longitude which inter-
sect at the point, thus, latitude 38°32'20" N., longitude
77°34'30" W. The latitude and longitude of a point constitute
its geographical or spherical coordinates. However, meridians

III A— 56

of longitude converge at the poles. Therefore, units of longi-
tude decrease in units of linear distance from a maximum
at the Equator to zero at the poles. Since the sphere cannot
be developed as a plane, other variations are introduced in
maps by the characteristics of projections used in map con-
struction. While units of latitude and longitude can be con-
verted to distances in meters, yards, miles, etc., by computation
or use of tables, the spherical units would not occur, except
by fortunate coincidence, in rational multiples of the linear
unit. Lines of the spherical grid are necessarily curves or
projections of curved lines and vary with latitude and pro-
jection. Such variations from straight lines and true distances
within the scope of a sheet of the terrain or the tactical map
are negligible. For practical map-reading purposes they
may be disregarded and the spherical grid may be treated
graphically in all respects as a rectangular grid. The 5-minute
lines of the geographic grid appear in full or by border
registration on topographic sheets. The 1-minute lines of the
geographic grid appear registered on some large-scale maps
by border ticks and grid intersections. Geographic coordi-
nates are used in designating positions in large indefinite
areas, in unmapped areas, and on geographic (ungridded)
maps.

On some sheets (for example, the Ft. Belvoir and Vicin-
ity, 1 :20,000) the overlap of the adjacent military grid zone is
also shown by a series of border ticks and grid intersections.
On maps of this type, great care must be taken in distinguish-
ing between the two grids.

a. To plot positions of point, geographical coordinates
of which are given. — (1) Identify on the map the two lines
of the geographic grid, both of latitude and longitude, which
fall nearest to and on each side of the position to be plotted.
This may be readily done by inspection of the map in com-
parison with the given coordinates. In case the lines of the
grid do not appear in full on the map, draw in the lines by
joining the border ticks and grid intersections. In either case
the point sought falls somewhere within the quadrangle whose
sides are lines (arcs) of known latitude and longitude. For a
battle map (1:20,000), this is a 1-minute quadrangle (60
seconds by 60 seconds). For a topographic sheet, this is a
5-minute quadrangle (300 seconds by 300 seconds).

(2) The problem then reduces itself to the me-
chanical operation of dividing the quadrangle into seconds of
longitude and seconds of latitude, pointing off the seconds
place required by each coordinate. One of these points will
fall on the meridian of longitude which passes through the
point sought. The other will fall on the parallel of latitude
which passes through the point sought. The significant
parallel of latitude and meridian of longitude are now struck
in as guide lines. Their intersection is the point sought.

Ill A— 57

(3) Points on the significant parallel of latitude
and meridian of longitude are readily located with the engi-
neer's scaie used as a diagonal scale of proportional parts
between the available grid lines. For the 1-minute grid the
scale should be placed across the lines at any angle so that
60 convenient divisions span the distance. For the 5-minute
grid 300 divisions of the scale should span the distance
between lines. In each case each division of the scale indicates
a second of latitude or longitude, depending upon which coordi-
nate is being plotted.

(4) Figure 27 illustrates the location of a point a,
the geographic coordinates of which are latitude 38°42'20" N.,
longitude 77°13'30" W.

b. To determine geographic coordinates of map posi-
tions. — (1) By inspection of the map, identify the grid
quadrangle in which the point lies, drawing in the sides of
the quadrangle when the grid appears registered only. The
value in degrees and minutes of the meridians of longitude
and parallels of latitude which form this quadrangle appears
in print on the borders of the map. The problem, then, is
to determine the position of the point within the quadrangle
in seconds of latitude and seconds of longitude.

Ill A— 58

1791

1790

1789

77° 14'

X -GRID LINE

1788

38° 43

= 38°42'

Figure 27. — Geographic coordinates: latitude 38°42'20"N., longitude
77°13'30"W.

(2) Use the engineer's scale as a scale of propor-
tional parts as described in Paragraph 43a (3) to establish the
seconds lines within the significant quadrangle, except in each
case (the two positions of the scale, one for latitude and one
for longitude, respectively) the scale should pass through the
point whose coordinates are desired. The number of seconds
sought may now be read directly from the edge of the scale
at the point in the direction of increasing grid values within
degrees and minutes of the side of the significant quadrangle
lowest in value yields the coordinate sought in degrees,
minutes, and seconds.

44. Military Grid System. — a. The standardized system of
rectangular coordinates discussed in paragraph 46 is the grid
system devised for use on military maps in order to avoid
the difficulties and inconveniences inherent to the spherical

III A— 59

grid. A rectangular grid superimposed on a polyconic pro-
jection of the whole continental United States would prove
no more useful than a map on that projection and for the
same reasons. Distances on the rectangular grid would vary
prohibitively from true ground distances in the distorted areas
near the edges of the map. However, by limiting the width
of the projection to about 9° of longitude, the maximum
distortion along the edge of the projection never exceeds 2.57
yards per 1,000 yards, or about V± of 1 percent, an error of
no military consequence, since the changes in dimensions of
an ordinary map sheet due to weather conditions may exceed
that amount.

b. For the purposes of superimposing the rectangular
grid, the northern half of the continental Western Hemisphere
has been divided into seven zones, each 9° of longitude wide.
Each zone is a separate polyconic projection. When the
military grid system was first established it extended from
28° N. latitude to 49° N. latitude. This system, known as the
continental system, was sufficient for continental United
States only. Later, in order to take care of Panama and the
Caribbean area, the equatorial system, extending from 7° N.
to 28° N., was set up. These two systems have different Y
origins, and hence any point in this area will have the same
X-Coordinate in both systems but different Y-coordinates.
All grids are identical in structure but each has a separate
origin 8° of longitude distant from its neighbor. The grids
therefore overlap 1° of longitude along the borders, with a
net width of 8° of longitude between the central meridians
of the overlaps. These zones are designated by a letter in
accordance with the following table, that portion of the
State of Maine falling to the east of longitude 68° 30' being
included in zone A. *

c. The limits of the grid zones are shown in table I.
The zone letter appears on all maps containing grids. In
designating points by grid coordinates, the name of the map
sheet and not the zone letter should be used as primary
reference.

Ill A—60

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III A— 64

45. Continental System. — a. In each zone the intersection
of its central meridian with the parallel of latitude 40° 30' is
selected as the origin of coordinates designated by 0. The
central meridian is chosen as the Y-axis and a right line
tangent to latitude 40° 30' at O is chosen as the X-axis. In
terms of yards, the grid coordinates of all 5-minute inter-
sections of latitude and longitude within the whole grid zone
are computed with respect to these axes and the origin O.
The coordinates of intersections in all other quadrants, except
the first, involve some negative quantities which are undesira-
ble for simplicity. In order to make positive all coordinates
which appear on military maps embraced within the zone,
the computed values are transferred to a new origin O' exactly
1,000,000 yards grid west and 2,000,000 yards grid south of
the origin O. This is effected by simply adding 1,000,000
yards to all computed X-coordinates and 2,000,000 yards to
all computed Y-coordinates. It is the point O' and axes O'-X
and O'-Y to which all grids and grid values appearing on all
military maps are related. The original origin O has no
further significance. This scheme is shown in Table I, and
the rectangular grid system illustrated therein is referred to
as the military grid system.

b. Since the grids for all zones are identical in struc-
ture, only one set of original computations suffices for all
zones simply by changing in the tables the longitude values
successively through 8°, 16°, 24°, etc., of longitude, respec-
tively. (See Special Publication 59, U.S. Coast and Geodetic
Survey.)

c. The military grid appears registered on gridded
maps in two series of parallel lines at right angles to each
other. On sheets of the terrain map (1:20,000), these lines
form 1,000-yard squares. On sheets of the tactical map
(1:62,500), these lines form 5,000-yard squares. The central
meridian of the overlap between adjacent grid zones is the
dividing line between the zones. Any map which falls within
the 1° overlap between grid zones always shows in solid
black lines the grid of the zone to which the map pertains.
The grid of the adjacent overlapping zone may also appear
registered by means of grid intersections (small crosses) on
the face of the sheet and ticks around the border lines. The
scheme is useful in effecting transition of data from one zone
to another. The lines of the overlapping zone when needed
may be struck in by simply joining the registration points.
Since the grid lines of each zone are all parallel to the central
meridian of the zone and since meridians converge to the
poles, the lines of overlapping grids will always cross at
distinct angles.

d. The distance of each north and south grid line,
grid east of the zero point or origin of coordinates, is marked
in thousands of yards along the south border of a gridded

III A— 65

map. The distance of each east and west grid line, grid north
of the zero point or origin, is marked in thousands of yards
along the west border of a gridded map. The numbers which
identify the north and south grid line and the east and west
grid line which intersect at or nearest to the southwest corner
of a gridded map are written out in full in yards. In marking
all other grid lines, the digits common to the sheet may
be omitted. When the grid of an overlapping zone appears
registered by ticks and grid intersection on a map, the ticks
of the north and south and east and west grid lines, respec-
tively, which intersect at or nearest to the southeast corner,
are marked in full to yards. No other grid lines of the over-
lapping zone are marked.

e. By agreement with the War Department, sheets of
the topographical atlas of the United States Geological Survey
adopted as tactical maps will have the 5,000-yard grid regis-
tered by ticks along the borders.

NOTE: The above methods of showing grids on a map are followed by
the Corps of Engineers in the reproduction of all gridded
maps. There are maps in common use for school purposes,
such as the Gettysburg map, on which only a local grid
system is used. The reader should not confuse such a grid
with the military grid system.

46. Equatorial System. — a. The equatorial system, using
the same zones as the continental system, has the latitudinal
origin at the Equator, and covers the area between the 7° N.
and 28° N. parallels. The system is otherwise similar to the
continental system. Tables and methods of computation for
the equatorial system are found in Corps of Engineers publi-
cation "Grid System for Military Maps for 7° to 28° North
Latitude."

b. In the overlapped areas below 28° N. in Texas
and Florida, care must be taken not to confuse the two grid
systems.

47. Military Grid. — a. General. — To make the reading of
military maps easy, grids are printed on the map. The grid
is simply a set of numbered north and south lines showing
distance in thousands of yards east of the origin, and a set
of numbered east and west lines showing distances in thou-
sands of yards north of the same reference point. On a
large-scale map (for example, 1:20,000 (par. 5) ) these lines
are 1,000 yards apart. On the medium-scale map (par. 5)
the lines are 5,000 yards apart.

b. Location by grid coordinates. — Points are designated
by coordinates simply by the intersection of the north-south
grid lines (vertical lines) with the east-west grid lines
(horizontal lines). Thus, in figure 29, location of the point
A is indicated by the intersection of the 198 grid line and 262

III A— 66

grid line; the coordinates of the point therefore are (198-262).
Note that distance east of origin is called the X-coordinate
and is read first; and that distance north of origin is called
the Y-coordinate and is read last. Beginners often make
the error of reading the wrong coordinate first. One way
to avoid this is to remember the key phrase "READ-RIGHT-
UP." It often may be necessary to designate points which do
not fall at the intersection of grid lines. For example, it is
required to find the coordinates of point B in figure 29. If it
is assumed that the sides of the grid square are further
subdivided into 10 equal parts, it is seen that the point B
is 8 of these parts east and 7 of the parts north of the
south-west corner of the square in which B is located. The
coordinates of the point B are therefore written (197.8-263.7).
Often sufficiently close determination can be made by esti-
mation. For example, CR (crossroads) 121 could be located
by inspection at (196.4-263.4). Since on all commonly used
large-scale maps the grid square measures 1,000 yards on a
side, a reading to tenths (one decimal place) gives a location
to the nearest 100 yards. A reading of hundredths (two
decimal places) gives an accuracy within 10 yards. When
the grid numbers have more than two digits, it is customary
to drop off all but the last two digits. Thus, the coordinates
of point B above may be written (97.8-63.7), or if greater
accuracy is desired (97.80-63.70).

121

-B

c

>r

-^

k

1

263

A-^

J^^^

A

IS

R.D. 3503

'6 1!

>7 l<

>8 l<

19

Figure 29. — Coordinates.

Ill A— 67

c. Location by grid squares. — When a point is easily

identified such as a numbered crossroad or a town, it is
necessary merely to refer to the southwest corner of the grid
square in which it is located. For example, in Figure 29 cross-
roads 121 could be designated as CR 121 (96-63).

48. Coordinate Scale. — a. General. — In paragraph 47, the
coordinates of point B were found by subdividing each side
of the square (197-263) into 10 parts. This operation is
used only for explanation and is too long and tedious for
normal use. A grid coordinate scale or card as shown in (1)
and (2), figure 30, permits finding these coordinates rapidly
and easily. These cards may be made of cardboard, metal,
or celluloid. For large-scale maps having grids 1,000 yards
apart, lay off on the interior edges 1,000 yards to the scale
of the map. Beginning at the vertex divide each 1,000 yards
into 10 equal parts. This may be done by means of the
graphical scale printed on the map. For medium-scale maps
having grids 5,000 yards apart, lay off on the inner edges
5,000 yards to the scale of the map, and subdivide each 1,000
yard division into 10 equal parts as described above. The
L-shape type is more convenient to use. However, the rec-
tangular type (1) and (2), (Figure 30) may be readily im-
provised by taking any square piece of cardboard or heavy
paper and laying it along the graphic scale at the bottom of
the map, mark off one corner with 1,000 yard divisions, sub-
dividing these into 100 divisions. (See Figure 31).

b. To read coordinates of any point on map using
coordinate scale. — Required, to find coordinates of point P (fig.
30). First identify the square in which P lies and write the
coordinates of the lower left (southwest) corner of the square
thus (1,365-1,791), or, dropping off the first two digits as
described in paragraph 47b, it could be written (65-91).
Now place the coordinate scale with its horizontal (east-west)
edge on the 1,791 grid line. Keeping this edge on the 1,791
grid line, slide the scale along until its north-south scale
passes through the point P. The decimal portion of the
X-coordinate is read on the horizontal (east-west) scale, where
it is cut by the west boundary of the square (in this case the
1,365 grid line). The decimal portion of the Y-coordinate is
read on the vertical (north-south) scale, at the point P.
These readings are then filled in at the proper places after
100 yards, the coordinates of P are (1,365.7-1,791.6) or (65.7-
91-6). Reading to the nearest 10 yards the coordinates are
(65.68-91.62). The coordinates of K are (65.25-92.48).

c. To plot on a map any point whose coordinates are
given. — This process is the reverse of determining the coordi-
nates of a point. For example, in Figure 30 let us assume that

III A— 68

it is required to plot the position of the point P whose coordi-
nates are (1,365.68-1,791.62). Place the coordinate scale on
the map as shown in position (1) in Figure 30. The position
of P can be marked at once with a pin or sharp pencil.

94

93

1000

20,000

9 —
8 —

7 —

6 —

500

3 —

— K

1000 500

19 8 7 6 14 3

2 1 -

1 1 I 1 i 1 1 1 1 1

-9

-8

-7

P —

-6

- 500

-4

-3

-2

III
19 8 7

1 1 1 1 1 1
6 14 3 2 10

1000

500

20,000

SO 3503

1364 65 66 67

Figure 30. — Plotting point with coordinate scale.

68

III A— 69

1000

Yards
500

p n q n n

!000

( Any Square Piece of
Paper or CaH Board)

(Graphic Scale)

Improvising a Coordinate Square

Figure 31. — Improvising a coordinate.

49. Thrust Line. — a. General. — A map-reference system of
location known as a Thrust Line is similar to a German map-
reference system called "stosslinie", which means thrust point.
In one sense thrust line coordinates are simply rectangular
coordinates with a "thrust line" substituted for a base position
and base direction. This thrust line is any line designated by
two points on the map. The points selected should be terrain
features easily located both on the ground and on the map.
The rear point is designated as the point of origin. The for-
ward point is called the extension point and establishes the
direction of the thrust line. The thrust line may be extended
indefinitely in both directions along the axis, and generally
points in the direction of the enemy.

b. Plotting Thrust Line Coordinates. — (1) The coor-
dinates of any point are obtained by dropping a perpendicular
from the point in question to the thrust line. The coordinates
are then read by measuring the distance from the origin to the
intersection of the perpendicular, and then from the intersec-
tion to the point in question. Distances forward of the origin
are preceded by the letter F ; distances back or to the rear of

III A— 70

the origin are preceded by the letter B. Similarly, distances
to the right of the thrust line are designated by the letter R
and distances to the left by the letter L.

(2) The unit of measurement can be established
by the commanding officer when he designates the thrust line,
or it may be established as standing operating procedure within
the unit. Either map distance or ground distance may be
used. If map distance is used, all maps concerned must be of
the same scale or tedious calculations will be involved, but if
ground distance is used, the coordinates will be the same on any
representation of the area regardless of scale as long as the
two points establishing the thrust line can be located. It is well
to use a graphic scale of the selected unit as a ruler to measure
distances on the map. The units to be used should always be
clearly stated at the time the thrust line is designated.

(3) Three digits are required for each measure-
ment; the last digit representing tenths of the unit of meas-
urement, although the decimal point is not shown.

T R.J. 243

BiMingsport School

MILES
E 3

RO 3509-1

Figure 32.— Thrust line: From CR 172 to RJ 243.
Ill A— 71

The thrust line is drawn from CR 172, the origin,
through RJ 243. This establishes the direction RJ 243 as for-
ward (F). Distances measured from the origin in the opposite
direction are back (B). The unit is stated as tenths of a mile.
Therefore, the coordinates of Billingsport School are F045R008
(forward 4.5 miles, right 0.8 mile) and the coordinates of St.
Paul's Church are B013L022 (back 1.3 miles, left 2.2 miles).
Notice that the decimal is not written but inferred.

Ill A— 72

SECTION 7
ELEVATION AND RELIEF

50. General. — a. Ground form and elevation. — Up to this
point the map has been regarded as a representation of a flat
surface and only the horizontal position of features indicated
thereon has been considered. A map to be of the greatest
practical value must convey to the user a definite impression of
ground forms (hills, ridges, and valleys) known as relief. This
brings up the important subject of elevations. By elevation is
meant the vertical distance of any specified point on the earth's
surface above a selected reference plane which for most maps
is mean sea level.

b. Means of representing relief and elevation. — Since a
map is a plane surface, some type of conventional sign must
be used in order to represent relief and elevation. On most
modern topographical maps, this is accomplished by the use of
contours. Other methods such as hachures and hill and valley
shading are used but contouring is the most common and
practical method.

51. Contours. — a. General. — Contours are the conventional
signs drawn on a map to show the different ground forms.
After practice with contours the map reader can not only
visualize shapes of hills, mountains, and valleys, but can also
find elevation of points and determine slope and visibility
along given lines. A contour is a line drawn on a map which
represents all imaginary line on the ground all points of which
are at the same elevation. Figure 33 represents a hill in the
middle of the ocean. The seashore line itself would be the
base or zero contour. If the sea should rise 10 feet the new
seashore line would mark the 10-foot contour. Similarly the
next higher contour line would be marked for each rise in
elevation of 10 feet. Figure 33 shows the successive increases
in sea level which indicate contours. Figure 34 gives an
oblique view of this same hill. From directly above, the hill
would appear as in Figure 35. Wiping out the picture of the
hill itself, it would appear on a map as in Figure 36 when
indicated by contours alone.

Ill A— 73

8.0, 3503

R. 0.3503

50 ft. HIGH

Figure 33.— Side view of hi

50 ft. HIGH

40 ft. HIGH
3 Oft. HIGH
20 ft. HIGH

IgTTHlGH
~BASE~~"

.....ft

■.. ..■■:■-■. " •■

Figure 34.— Oblique view of hill.

Ill A— 74

'

:■■&';

R.D 3503

50 ft. HIGH
4 ft. HIGH
30 ft. HIGH
20 ft. HIGH

Figure 35. — Top view of hill.

R.D. 3503

Figure 36. — Hill shown by contours.

Ill A— 75

b. Characteristics. — Figure 37 represents a number of
more common ground forms as they are shown by contours.
Looking at this figure it should be noted that —

(1) Contours have a characteristic appearance of a
series of generally smooth curving lines (except in very rugged
country).

(2) Elevation of contours above the reference
plane (mean sea level) is shown by numbers usually in feet.

(3) At A, B, and C are contours which are closed
curves, indicating either hilltops or depressions. Since the
contour numbers increase as these points are approached it
is apparent that A, B, and C are actually on hilltops.

(4) Contour at A, being nearly circular, indicates
the top of a peak or knob, whereas the elongated contour at C
indicates the crest of a sharp ridge.

(5) Though all contours are closed curves, most
of those shown do not close within the limits of the map
sheet. The 200-foot contour runs off the sheet at D-D and
closes just outside, as indicated by the broken line. It runs
off again at D'-D' and closes beyond limits of the sheet.

(6) On the line AA' there is a uniform slope.
This is indicated by the equally spaced contours. On the
line BB' there is a concave (sway-back) slope since the con-
tours are close together at the top and farther apart at the
bottom. On the line CC there is a convex (humpback) slope.
At B there is a steep slope while at B' there is a gentle slope.
The representation of these slopes by means of profiles is
further illustrated in Figure 45. (For construction of profiles
see paragraph 64.

(7) Contours do not touch each other except at E,
which indicates a vertical cliff.

(8) At the points marked X is seen the character-
istic V-shape of valley or streamline contours, and at those
points marked U, the U-shape of ridge contours. The closed
ends of the V's point upstream and those of the U's downhill.

(9) At A' is shown the characteristic M-shape
appearance of the contour at a Y-stream junction.

(10) Rain falling at I runs down the slope normal
to the contours, entering the drainage line near G, and ulti-
mately leaving the area by the main stream at J. The line
of the spur AA' is the divide between the two tributary
streams. Rain falling at K, just east of the divide flows
into the eastern tributary. The divide between any two
adjacent valleys is easily traced out.

(11) Point S is a saddle, a depression or low point
in a ridge or line of hills. Note the characteristic shape of

Ill A— 76

Figure 37. — Characteristics of contours.

(12) Adjacent contours in a water-worn terrain
resemble each other. This is the same as saying that changes
in the form of the ground are gradual. This characteristic
may be noted at many places, as on the ridge lines at AA'
and BB'.

c. Summary. — Briefly summarized, contour character-
istics previously discussed and illustrated are —

(1) A contour is a line on a map joining points of
equal elevation.

(2) Contours are spaced at uniform vertical
intervals.

(3) A small closed contour indicates a hilltop or
a depression when so marked by the conventional sign.

Ill A— 77

(4) Every contour is a continuous closed curve, on
or off the map.

(5) Spacing of contours indicates steepness of
slopes. This spacing also indicates nature of slope, whether
uniform, concave, or convex.

(6) Contours do not touch or cross each other,
except in the unusual case of cliffs.

(7) Valleys are usually characterized by V-shaped
contours, and ridges by U-shaped contours.

(8) Adjacent contours resemble each other.

52. Contour Interval. — a. The contour interval, or the
vertical distance in feet between one contour and the next
is stated as marginal information, usually under the scale at
the bottom of each map. This interval differs according to
the topography of the area mapped and the scale of the map;
in a flat country it may be as small as 1 foot ; in mountainous
region it may be as great as 250 feet.

b. For military use it is necessary that the various
sheets of a map of any given area have a common scale and
contour interval or intervals that match. In order that peace-
time practice throughout the United States be consistent, the
War Department (AR 300-15) and the United States Geologi-
cal Survey have adopted the following contour intervals for
standard quadrangle maps. The intervals in general conform
to contour intervals found on most existing topographic maps.

(1) Contour intervals of 5, 25, 50, or 100 feet in
the States which lie all or mostly west of longitude 103° as
follows : Washington, Oregon, California, Idaho, Nevada, Utah,
Arizona, Montana, Wyoming, Colorado and New Mexico.

(2) Contour intervals of 5, 10, 20, 40, or 100 feet
in the States which lie all or mostly east of longitude 103°.
The 5-foot contour intervals is used only on large-scale maps
of limited areas.

c. On most maps every fifth contour line is made
heavier than the others and is accompanied by figures showing
the altitude at convenient intervals.

53. Elevations of Important Features. — The elevations of
important features such as road junctions, summits, and sur-
faces of lakes, called spot heights, and those of bench marks
are given on the map in figures to the nearest foot. More
exact altitudes of bench marks are published in bulletins that
are issued by the Geological Survey and the Coast and Geo-
detic Survey. On coastal charts the datum is mean low water.

54. Logical Contouring. — a. In mapping, contouring may
be done by the topographer in the field by one of several
methods :

(1) He may actually run out the location of the

III A— 78

contours on the ground. This method is applicable to large-
scale maps when great accuracy is desired and the expenditure
of time and labor is economically justified.

(2) He may run out enough contours to define the
ground forms and interpolate between them by eye.

(3) He may run out only stream and ridge lines,
getting elevations on these lines at each change of slope or
ground form. Such elevations defining the ground forms are
known as "critical elevations." The contours may then be
sketched in the field by eye between critical elevations. This
method is the cheapest, quickest, and most commonly used.

b. Logical contouring may best be explained by an
illustrative example. In Figure 38 ® critical elevations have
been measured by the topographer. The problem is to inter-
polate 10-foot contours so that the ground forms depicted will
be logical.

(1) First, along the main stream, interpolate the
elevations of all stream junctions not shown by assuming
that the stream has a uniform slope between critical points.
For example, there is a stream junction of unknown elevation
between elevations of the stream of 91 and 97 feet, respec-
tively. Between these two points the stream rises 6 feet.
Because the stream junction, the elevation of which is sought
is approximately half the distance measured along the stream
between elevations 91 and 97, it is assumed that the stream
has risen to that point only one-half of 6, or 3 feet. The
elevation sought is therefore 94 feet.

(2) In this way, interpolate elevations which are
multiples of 10 feet on all the streams. These are the points
where contours cross the stream and are shown as V-shaped
marks pointed upstream as in Figure 38 ©.

(3) By interpolation between critical elevations
determine where 10-foot contours trace the ridges and indi-
cate by slightly drawn LPs. Since hills are normally rounded
at top and slope off gradually at the bottom, contours will
have slightly closer spacing on the rise than at the crest or
bottom.

(4) Consider the importance of all critical points
in relation to each other, remembering that ground forms
between generally parallel streams are in the form of ridges,
terminating in spurs or noses.

(5) Starting at the lower end of the main stream-
line and using the drainage system as a skeleton upon which to
shape the contours, connect all interpolated points of the same
elevation with a smooth, curved line, continuing each contour
line until it runs off the map or closes on itself.

(6) Every fifth contour (starting from 0) should
be made heavier than the rest and should have the elevation
written on it.

Ill A— 79

x 130

X

i

128

xl32

X

1

110

S

110

i

97^

^98

^x 125

-*9I

x 132

'\

>90

'••x 120
x!30

'••— -xl35

x 140

xl30

x

T

28

XI32 7

y

>T

no

^*no

— '

""*9I

— \00'

-*98

. \ ^ -x 125

/ /xl32

/*90

/

y

<

'■^120

130

'•— xl35
xl40

__^^s^y

/iv.

y^ . ^ — i2o—^

^^ JL

*^ • \ . ;>> • " y

y/ [00^

^° o ^"

rrr

^^ ^^^~ ^

/^ ^^ ^f

/^

2^J V

^^^~

_|40

RD 3503"

^
W

Figure 38. — Method of drawing contours by interpolation on drainage
net where elevations are given.

II A— 80

c. Contouring a saddle. — One of the few ground forms
that may cause difficulty in contouring- logically is the saddle.
In order to recognize the existence of saddle when only the
critical elevations are given, remember that five points are
needed to determine a saddle and that a saddle is the low
point between two high points and is also the high point
between two low points. These five points are connected in a
diamond or kite-shaped pattern and interpolations are made
along all these lines. If this method is followed as illustrated
in Figure 39 it greatly simplifies the contouring of saddles.

118 x

178
X

X

142

X
183

178

118 x>

142

X III

x

183

178

i x|||

Figure 39. — Contouring a saddle.

d. The contours should be sketched while in the field.
However, if enemy action or other cause makes this impos-
sible, contours may be interpolated in the office, preferably
with the aid of aerial photographs and a stereoscope, provided
that critical points have been adequately determined.

Ill A— 81

55. Determination of Elevation. — a. In the discussion in
paragraph 53, elevations of important features on the map
were determined by their spot heights. Where accurate ele-
vations of other points are desired, some means of interpola-
tion between contours becomes necessary. In the following
procedure the refinement is for theoretical purposes only. Any
interpolation from contours is an approximation upon which

b. Refer to the margin of the map. To determine the
elevation of any specific point, proceed as follows (fig. 40) :

(1) If the point falls on a heavy contour, it is
only necessary to follow that contour until the elevation ap-
pears and read it. For example, the elevation of the point B
in the figure is read directly as 1,300 feet.

(2) If the point falls on a light contour, the ele-
vation is found by reference to the adjacent heavy numbered
contour lines and interpolating. For example, the elevation
of the point A is 1,260 feet.

(3) When the point lies between two contours as
at C in Figure 40.

(a) Find the elevation of the nearest contour
line.

(b) Measure the shortest distance between
the two adjacent contours along a line passing through the
point C.

(c) Measure the distance along this line from
the point in question to the nearest contour.

(d) Solve the following equation:
Distance from point to nearest contour
X contour interval

Distance between contours
= difference in elevation between point in question and the
nearest contour. Since the distance between adjacent contours
at this place is 375 yards and since C is 125 yards from the
nearest contour (the 1,260 contour), entering the equation
given above,

125
X 20 feet = 6% feet.

375
Taking the nearest whole number of feet (7), the elevation
at point C is 7 feet less than the elevation of the nearest
contour, or 1,260 — 7 = 1,253 feet. If the nearest contour is of
lower elevation than the point in question, the difference in
elevation must of course be added.

(For all practical purposes the interpolation between
contour lines may be estimated by eye without recourse to
the above method.)

Ill A— 82

(4) When a point, the elevation of which is re-
quired, lies within a closed contour forming the top of a hill,
ridge, or nose, or the bottom of a depression, only an approxi-
mation of its actual elevation is possible. Consider the eleva-
tion in respect to probable ground form obtained as indicated
by the spacing of adjacent contour lines.

CONTOUR INTERVAL 20 FEET

R.D.3503

Figure 40. — Determination of elevation on contoured map.

56. Ridge Lining and Stream Lining. — a. Purpose. — In

order to emphasize the basic structure or master lines of the
terrain of a given area, a system known as ridge lining and
stream lining is often used. On a map or an aerial photograph
thus ridge lined or stream lined, the great mass of detail which
may tend to confuse may be neglected for the moment, and
those basic structures such as stream systems, ridge lines,
and key features can be emphasized. Three steps may be
followed in this process.

b. Stream lines. — Study the map or aerial photograph
and select the main streams and their tributaries. Emphasize
them, preferably by drawing over them in blue, and thus cause
the drainage system to stand out.

The drainage net is the key to the topography.

c. Ridge lines. — Draw a line down the main ridges.
This should be done preferably in red so as not to obscure
features lying under the lines. Then select the minor ridges
and trace their ridge lines in a similar manner. The number
of minor ridges to be included will depend upon the emphasis
desired. In drawing ridge lines it is not normal to carry them
all the way to the stream. A good system is to stop at the

III A— 83

beginning of the flood plane as shown by the increase in space
between contours. It will be noted that the tendency at first
is to mark isolated ridges, whereas the ridge lines should form
a connected structure. If all the ridge lines in an area are
drawn, it usually will be found that they join together into a
systematic branching structure like the fingers of a hand or
the backbone and smaller bones of a fish. This structure is
similar also to the branches of streams ; in fact the branches
are fingers of the two systems fitted into each other. Ridge
lines do not cross streams. Figure 41 shows a portion of a
contour map which has been ridge lined. Note how the main
drainage system and the main ridge lines stand out.

d. Emphasized contours on contoured maps. — Certain
contours may be emphasized by use of thicker lines, and it is
customary to do this at regular intervals to facilitate the read-
ing of contour maps. Likewise, commanding elevations may
be brought out by coloring the map area between selected
contours.

Ill A— 84

R D 3503

Figure 41. — Ridge and drainage lines.

Ill A— 55

SECTION 8
SLOPE, PROFILE, AND VISIBILITY

57. Slope. — The inclination of the land surface relative to
a horizontal plane is the slope, and slope is a function of two
factors — horizontal distance and vertical distance. Two points
are therefore necessary to determine these factors. The verti-
cal distance is the difference in elevation of the points and on
a contoured map may be interpolated from the contours. The
horizontal distance is scaled from the face of the map. Along
a straight line it is the scaled length of the straight line.
Along a meandering stream, irregular road, or broken line, it
is the scaled length of the meander line or other irregular
distance under consideration. Both horizontal and vertical
distance must be expressed by the same units, preferably feet.
Slope may be computed or measured and expressed in terms of
used method of expressing slope is by percent, the advanced
map reader should be familiar with other methods.

58. Slope in Percent. — Percent is the most convenient and
commonly used method of expressing slope. A slope of 1
percent is a slope which rises vertically a distance of one unit
in a horizontal distance of 100 units or one which has this
rate of rise (Figure 42). A 2-percent slope rises two units, a
3-percent slope rises three units, and so on, in a horizontal
distance of 100 units. The value in percent of any slope is
the number of units which it rises vertically in a horizontal
distance of 100 units. Thus a rise of 26.8 feet in a horizontal
distance of 100 feet is a slope of 26.8 percent.

59. Slope in Mils. — The mil is a unit of angular measure-
ment. A true mil is an angle which subtends an arc of unity
at a radius of 1,000 units (Figure 42). A 2-mil slope subtends
an arc of two units, a 3-mil slope subtends an arc of three
units, and so on, at a 1,000-unit radius. The value of slope in
mils is therefore a function of the angle of slope. The vertical
rise of a mil slope is not exactly equal to the subtended arc, the
vertical rise of a slope of 2 mils is not exactly twice the vertical
rise of a slope of 1 mil, and the variation increases with the
angle of slope. However, for slopes up to 350 mils, the varia-
tions are inappreciable and may be disregarded for average
purposes. Thus a slope which rises 268 units in a horizontal
distance of 1,000 units is a slope of 268 mils (Figure 42) . Slopes
may be measured with instruments graduated in the arbitrary
mil which is 1/6400 of a circle. For ordinary slopes the
results would not differ appreciably from the value in true
mils, of which the circle contains approximately 6,283.

Ill A— 87

>\0

PROJECTION OF A AND B ON THE MAP.

Horizontol Distance = 100 Units

EXPRESSED AS GRADE IN PERCENT = 26.80% B

Rise 268
Units

EXPRESSED IN DEGREES = +I5°A TO B, -I5°B TO A B

I Rise I Unit

Horizontal Distance = 3.7 Units

EXPRESSED AS A GRADIENT = 26.80 ON 100=1 ON 3.7

Figure 42. — Determination and expression of slope between two points
"A" and "B" on map.

Ill A— 88

60. Slope in Degrees. — Many instruments for measuring
slope are graduated in degrees. The degree is a unit of angu-
lar measurement and is 1/360 of the circle. A degree is an
angle which subtends an arc of unity at a radius of approxi-
mately 57.3 units (Figure 42). A 2° slope subtends an arc of
two units, a 3° slope subtends an arc of three units, and so on,
at a 57.3-unit radius. The value of slope expressed in degrees
is therefore a function of the angle of slope (Figure 42). The
vertical rise of a degree slope is not exactly equal to the sub-
tended arc, a slope of 2° is not exactly twice the vertical rise
of a 1° slope, and the variation increases with the angle of
slope. However, for slopes up to 20° the variations are
negligible and may be disregarded.

61. Gradient. — The gradient is the unit usually used in the
measurement of steep slopes. It is the ratio of vertical to
horizontal or of horizontal to vertical distance (Figure 42) . The
manner of expressing this ratio has not been standardized.
Two methods are in common use as follows : A gradient of 1
on 3.7 and a gradient of 3.7 to 1.

62. Slope Between Two Points on Map. — a. Subtract the
elevation of the initial point from the elevation of second point
to determine the difference in elevation or vertical rise.

b. Scale from the map the horizontal distance between
the two points along the line whose slope is to be determined
and express in the same units of measurement, preferably
feet.

c. Compute the value of slope from the appropriate one

of the following formulas :

x -v .„ difference in elevation X 100

(1) Percent = —

(2) Mils =

(3) Degrees

horizontal distance
difference in elevation X 1,000
horizontal distance
difference in elevation X 57.3

horizontal distance
difference in elevation

horizontal distance
expressed as a fraction reduced to simplest
terms.

63. Average Slopes. — In determining slopes by the methods
and formulas described, it should be remembered that the re-
sult expresses the slope of an inclined plane surface, whereas
the actual surface of the intervening ground may vary quite
irregularly up and down. It is therefore customary to refer
to slopes thus determined between points over broken terrain
or irregular surfaces as "average slopes."

64. Profile. — a. General. — The most satisfactory way of
showing the slope of any line on a map is by drawing its profile.

Ill A— 89

A profile between two points is the line (usually irregular)
of intersection of an imaginary vertical plane cutting the
earth's surface between two points. For example, in Figure 43
imagine a vertical plane passed from above through the earth
between the points A and B, and the front half of the hills
and the ridges removed, just as a cook passes a knife through
a cake and removes half. The outline of the surface of the
remaining half would be its profile as represented in Figure
43 © . Profiles are also a means of determining the visibility
or the defilade of points or areas from any selected point on a
map. Visibility is discussed in paragraph 65.

b. To draw profile between two points. — Figure 43
represents a portion of a contoured map. It is desired to
construct the profile of the giound represented by the map
between the points A and B. Proceed as follows:

(1) Connect points A and B by a straight line
and assume that a vertical plane is passed through this line.

(2) Take a piece of cross section paper or any
paper which has parallel lines equally spaced; cut or fold
the paper along one of these lines.

(3) Refer to map and determine the highest and
lowest elevation along the line AB; number the spaces on
the paper to correspond with the elevations on the map
beginning with the highest elevation toward the top edge of
the paper (fig 43).

(4) Place the top edge of the paper along the line
AB and where the edge intersects each contour, drop a perpen-
dicular to the horizontal line on the paper corresponding to the
elevation of the contour being considered. Proceed in the same
manner with each contour.

(5) Connect the points of intersection of the per-
pendiculars with the lines on the paper with a smooth, curved
line. This will represent the profile except between adjacent
contours of the same elevation which require the determina-
tion of intermediate elevations.

(6) Where the line crosses a crest or a depression
an elevation number on the map is sometimes found to assist
in completing the profile. Where such elevation numbers
are missing, interpolate necessary elevations from the spacing
of the contours.

(7) When a profile is desired of an irregular line
on the map, such as a road or trench, divide it into a series of
sections approximately straight and plot as directed above,
turning the paper at each angle to make a continuous profile.

c. Vertical scale. — Profiles usually have an exaggerated
vertical scale in comparison with the horizontal scale which
ordinarily is the same as that of the map as shown in Figure

III A— 90

43. In the figure, the lines on the paper could represent 10-
foot elevations indicated, or they could represent 5-foot ele-
vations, thus further exaggerating the profile as desired.
For constructing profiles, use of cross section paper will be
found most convenient since the vertical lines assist in drop-
ping the perpendiculars to the horizontal lines representing the
contour elevations.

EDGE OF PAPER

Figure 43. — Construction of a profile.

Ill A— 91

65. Visibility. — a. General. — One of the important uses of
maps for military purposes is to determine whether a point,
a route of travel or an area is visible from a given point or
position. The extent of the area visible affects selection of
targets, siting of weapons, and location of defiladed area or
dead space (Figure 44). There are various methods of solving
visibility problems but only the ones more commonly used
will be covered in this text.

b. Inspection. — Many problems of visibility may be
solved by inspecting the map, and determining from the con-
tours the ground slope represented. The representation of
ground slopes by contours is described and illustrated in
paragraph 51. For example, in Figure 44 it is evident by inspec-
tion that an observer at B cannot see the ground at A, this
being a convex or humpback slope, while an observer at C
can, this being a concave or swayback slope.

Topographical
Crest

c. Profile. — In paragraph 64 it was learned how to
construct a profile between two points such as AB on Figure
43. Suppose it is required to use the profile method to deter-
mine what points along the line AB are visible from an
observer at A. Construct a profile along the line AB as
described in paragraph 64. It is evident in Figure 45 that the
portion of the profile that is shaded is not visible from an
observer at A.

d. Hasty profile. — Many problems of visibility may be
solved without drawing a complete profile. In such cases
only the critical points which may affect the visibility are
plotted, such points being first determined by inspection.

ill A— 92

EDGE OF PAPEF

s~ Line of sight, A to mask C

Figure 45. — Determination of visibility by profile method.

These points would be the position of the observer's eye, the
probable masks (hills and ridges), and the point where
visibility is to be determined. This is illustrated in Figure
46 which represents a portion of a contoured map. It is
required to determine what an observer can see along the
line AP from various points along this line, assuming trees
and other vegetation do not interfere. It is evident that
while at A the observer can see only point B and point F.
From B he can see A, C, E, and F, but is unable to see points
D and P. This can be continued for other points.

Ill A— 93

-320

Figure 46. — Determination of visibility by hasty profile method.

e. Defiladed Areas. — It is often desirable to know the
area that is defiladed from observation from a certain point.
This defiladed area may be plotted on the map by extending a
series of lines in a spoke-shaped pattern from the point in
question. Profiles may then be constructed along each of these
lines or radii. The line of sight from the point of observation
is then drawn in and the defiladed or dead space along this line
is then projected back onto the line on the map. The series
of defiaded lines of sight are then connected logically with a
crosshatched. (See Figure 47).

ill A— 94

Ill A— 95

SECTION 9

66. General. — All students should keep in mind the im-
portance of being able to read maps accurately and quickly in
the field. Many disastrous mistakes have resulted from a
lack of ability to read maps. To be able to read a map properly
in the field, the student should be familiar with all material
covered in the preceding sections. He should keep in mind
that the map and aerial photograph are often the only means
available for studying distant or inaccessible areas. He
should always take his map into the field with him and con-
stantly refer to it. He should keep his movements plotted on
it, especially when operating over unfamiliar territory, and
verify his location at every opportunity. He should practice
until it is possible for him to secure a clear and accurate pic-
ture of the ground from the information given on the map.
In addition to material in preceding sections, a few aids to
his map reading ability are orientation, use of compass, deter-
mination of distance, and names by which ordinary features
of the ground are known. A brief description of each of
these follow.

67. Orientation. — a. Definition. — A map is oriented when,
in a horizontal position, its north point points north and all
lines of the map are parallel to the corresponding lines of the
ground. A map reader is oriented when he knows his posi-
tion on an oriented map and the cardinal directions on the
ground. A map will be of small use in the field unless its
command of the simpler methods of practical orientation is
of prime importance to the student of map reading.

b. Method of map orientation. — (1) Inspection. —

Figure 48 shows how a map may be oriented by carefully
observing road system and features in immediate vicinity.
It will be noted that the map has been rotated horizontally
until the road on the map parallels the road on the ground,
care being used to see that positions of nearby ground fea-
tures are in similar relation to their corresponding conven-
tional signs as shown on the map. This is the most practical
method of ordinary purposes and may be used as a rough
check on more accurate methods.

(2) Compass. — Magnetic north is shown on most
maps and is also indicated in the field by the north end of the
compass needle. Figure 49 illustrates use of this method.
Either prolong magnetic north line or draw a line parallel to it.
Then place compass on map with north point of compass
case on this line. Rotate map horizontally until north end of
needle coincides with north point of the case. Map is now
oriented.

On gridded maps the compass may be placed on the
Y grid line and map rotated until the compass needle points
to prevailing magnetic north as set forth in map marginal data.

Ill A— 97

R 0.3503

Figure 48. — Orienting map by inspection.

(3) By means of a distant point when observer's
position is known. — A third method of orientation where a
compass is not available and where there are no nearby fea-
tures suitable for orientation by inspection is illustrated in
Figure 50. Place a pin at observer's position on map. This
may be found by reference to the fence corner (Figure 50).
Place another pin on the map location of some well-defined point
such as the church. Holding map horizontal, sight at church
on the ground along the line of pins. Map is now oriented.
A more precise orientation is secured if more than one point
can be used. Once the map is oriented, approximate map
location of a target or other point may be determined as fol-
lows: keeping map in oriented position, sight over pin at
observer's position toward designated point and place a pin
on line of sight. From a study of the map or by estimation or
measurement of the distance fix location of the point.

Ill A— 98

Figure 49. — Orientation of maps by compass.
Ill A— 99

Figure 50. — Orienting map by means of distant point.

68. Finding Observer's Position on Map. — a. Inspection. —

If approximate location on a map is known, all the observer
has to do is study visible terrain for distinctive features and
his position can be found by identifying these features on
the map. This procedure is greatly simplified if the map is
oriented to the ground. Figure 51 is an example of this
method.

b. Striding or estimation of distance when along road,
railroad, etc. — This method is illustrated in Figure 52. Briefly,
the method is to identify on the ground the nearest road
bend, road junction, bridge, etc., which appears on the map,
such as B in Figure 52. The distance to this point is either
estimated or measured by striding and position on the map is
obtained by laying off distance AB to scale of map as indicated
in the sketch.

Ill A— 100

POSITION 01
OBSERVEI

Figure 51 .—Locating position on map by inspection.

c. One Point Resection. — Location of one's position
along road or similar feature by sighting on distant point. —

The position may be determined graphically or may be plotted
by means of a protractor after a compass has been used to give
direction. The first method is the speedier and is most com-
monly employed when the determination of position is under-
taken in the field.

(1) Graphic method (Figure 53). — Proceed as fol-
lows:

(a) Identify a convenient visible object B on
the ground which appears on the map at b.

(b) Rest the map in a horizontal position on
some nearby convenient support, such as a fence post, stone,
or fold in the terrain, from which B is visible, and set a pin
in the map at b.

(c) Orient the map.

(d) Without moving the map, hold a straight-
edge against the pin at b and aline its edge with the object B
on the terrain.

Ill A— 101

MAP

DISTANCE AB LAID
OFF ALONG be TO
SCALE OF MAP THUS
LOCATING o.

R.D.3503

Figure 52.— Location of observers position on map by striding or esti-

(e) Draw a line through b along the straight-
edge and prolong it to intersection with the road at a. This
intersection is the point sought.

(2) By means of compass and protractor (Figure
54). — Proceed as follows:

(a) Identify a convenient visible object B on
the ground whose position b appears on the map.

(b) With the compass, sight B and read the
magnetic azimuth.

(c) On the map with the protractor lay off
this azimuth through b and prolong the line until it intersects
the road at a, which is the position sought.

Ill A— 102

LINE OF SIGHT

TO B

STRAIGHTEDGE

R.D.3503

Figure 53. — Location of ones position on map by resection when along

Ill A— 103

MAGNETIC AZIMUTH
B MEASURED AT A"

NOTE: Mop need not be oriented.

POSITION OF

R.D. 3503

Figure 54. — Location of ones position on map by resection when along

NOTE: When azimuths are read from observer to a known position,
either the azimuth or back azimuth may be used in plotting
the direction line through the known position.

Ill A— 104

d. Two Point Resection. — Location of one's position by
resection from two distant points. — This method of locating a
position is useful when no well-defined feature, such as a road,
is in the vicinity. The position may be determined graphically
or may be plotted by means of a protractor after directions
have been read by a compass. The first method is speedier and
is most commonly employed when the determination of position
is undertaken in the field.

(1) Graphic method (Figure 55). — Proceed as fol-
lows:

(a) Select two visible objects on the terrain,
as B and C, whose positions b and c appear on the map, so
situated that lines radiating from observer to objects form
an angle of 30° to 150° at the observer.

(b) Rest the map in a horizontal position on
some nearby convenient support, such as a fence post, stone,
or convenient fold in the terrain, from which the objects B
and C on the terrain are visible and set pins through their
respective map positions, b and c.

(c) In this position, orient the map.

(d) Without moving the map, sight B and
C successively on the terrain along a straightedge held
against the pins through the corresponding points b and c,
respectively. Along the straightedge, draw lines through b
and c and prolong these lines to intersection at a, which is the
point sought.

(2) By means of compass and protractor (Figure
56). — Proceed as follows:

(a) Select two visible objects on the ter-
rain, as B and C, the positions of which, b and c, can be identi-
fied on the map and which are so situated that lines radiating
from observer to object make an angle of 30° to 150° at the
observer.

(b) With the compass sight the objects on
the landscape successively, reading the magnetic azimuth to
each.

(c) Draw magnetic north guide lines
through the map position of each object, b and c, and with the
protractor lay off the respective magnetic azimuths.

(d) Prolong the azimuth lines through the
points b and c until they intersect.

(e) The intersection of these lines at a is
the map position sought.

Ill A— 105

Figure 55. — Location of ones position on map by resection from two
distant points (graphic method).

Ill A— 106

MAGNETIC AZIMUTH OF
B MEASURED AT A

1 B

MAGNETIC AZIMUTH OF
C MEASURED AT A

X

h-
tr
o

2
O

lii

Z

o

<

A

/^

^^^^wAs

X

i-

IT

o

z
o

t-
u

z
a
<

(

±fb MAP

1

c

R.0. 3503

NOTE". Map need not be oriented.

Figure 56. — Location of ones position on map by resection from two
distant points, using compass and protractor.

Ill A— 10'

e. Three Point Resection. — Location of one's position
by resection from three distant points (tracing paper method)

(kg. 57) . — This method is useful on unoriented maps when the
observer is without a compass in indefinite terrain of which
only distant prominent features are recognizable or when local
attraction due to presence of ore bodies or other material ren-
ders the magnetic needle useless.

(1) Select three visible objects on the terrain
such as A, B, and C, so distributed that radial lines drawn
from observer to each point will yield good angles of intersec-
tion (about 30° to 150°) at 0, the position occupied by the
observer (fig. 57 (1) ).

(2) Place a piece of tracing paper on a flat surface,
supported on a convenient fence post, rock, or on the ground
and set a pin in it at any convenient assumed position of the
observer at 0.

(3) Place any suitable straightedge against the
pin, sight along its edge successively to each object, A, B,
and C, on the terrain and draw radial lines along the straight-
edge toward each object (Figure 57 (2) ) .

(4) Remove the tracing paper and superimpose it
on the map, shifting it about until the three radial lines pass
through the conventional signs a, b, and c on the map which
correspond to the three objects sighted on the ground (Figure
58).

(5) In this position, prick the map through the
original pinhole o on the tracing. The point thus located on
the map is the position of the map reader.

NOTE: There is only one possible position in which the overlay can be
placed so that the three radial lines pass through their re-
spective positions.

Ill A— 108

I btaa

# jf-'Ht

W **'''' -At

#*

*i^

1 f

Figure 57. — Three point resection in the field.
Ill A— 109

Figure 58. — Locating position on a map by tracing paper overlay.

Ill A— 110

69. Two Point Intersection. — Location of Distant Point by
Intersection. — a. With compass and protractor. — It is fre-
quently desirable to locate or post on a map distant or inac-
cessible objects on the terrain which do not appear on the map
in hand. This may be conveniently done by intersecting lines
from two occupied points of known position on the map. As-
sume that the location of an object C shown in Figure 59 is
desired on a map. In order to locate the position of C, one must
occupy successively two positions, such as A and B, from
which the object C is visible and read the magnetic azimuth
of C from A and B, respectively. By aid of a protractor, these
azimuths are plotted through the corresponding positions a
and b on the map. The direction lines prolonged will intersect
at c on the map, the position sought. Many points may be thus
located on the map from two occupied positions.

b. Graphic method (Figure 60) . — The observer occupies
in succession the positions A and B on the ground. In each
position he rests the map horizontally on some nearby con-
venient support and sets a pin in the corresponding map posi-
tions a and b, respectively. In each position the map may be
oriented with a compass, by inspection, or by alining the posi-
tions a and b on the map with the corresponding objects A
and B on the ground. The last method is the most accurate.
At each occupied position a straightedge is placed against the
pin in the corresponding position on the oriented map, the
object C, the position of which is sought, is sighted along the
straightedge and a direction line drawn thereto. This results
in two such direction lines, one from each occupied position,
the intersection of which gives the map position c of the
object C. The results may be checked by a direction line
from a third position of the observer.

Ill A— in

MAGNETIC AZIMUTH

OF C/
MEASURED AT
A = 30°

MAGNETIC AZIMUTH
\ OF C
MEASURED AT
vB = 325°

MAP

NOTE -Map need not be oriented

R.D.3503

Figure 59. — Location on map of distant point by intersection, using
compass and protractor.

Ill A— 112

Figure 60. — Location on map of distant point by intersection (graphic
method).

70. Traverse. — a. A series of lines of known distance and
direction is called a traverse. An approach route to an assem-
bly area, designated with distances and directions from point
to point, would form a traverse.

b. In locating on the terrain objects which do not
appear on the map and which cannot be intersected, or in
exploring unfamiliar terrain equipped with a compass, the
method of traversing is useful. This consists of starting
from a known point and following observed compass courses
from point to point, measuring- distances. These course lines
and distances when plotted to scale on the map, show graphi-
cally the course followed and the map location of any desired
point on the traverse. Where the distance to the point sought
is great and the intervening terrain is rough, it is not practi-
cable to attempt its location by means of a simple straight
course. In such cases the traverse would consist of a meander
of many straight course lines and angles making changes of

III A— 113

direction as influenced by the intervening terrain but ulti-
mately terminating at the point sought. Scouts use this
method in registering on a map the route they follow.

71. Compass. — a. Types. — The three types of compass
issued in the service are prismatic, lensatic, and watch. The
watch compass is being replaced by the lensatic compass;
descriptions of the other two types are given below.

(1) Prismatic. — The prismatic compass is shown
in Figure 61 showing the more important parts labeled. It
consists of a case containing a magnetic dial (b) balanced on
a pivot, a hinged cover (d) with a glass window, a holding
ring (e) and an eyepiece (a) containing a prism for reading
graduations on the dial. The dial has two scales, the outer
scale to read through the prism or eyepiece and the inner to
The north point is indicated by an arrow of luminous paint.
The glass cover has an etched line (f) which may be used
like a front sight, and the eyepiece (a) has a slot that may be
used as a rear sight. In case the window in this cover is
broken, a horsehair or a fine wire can be threaded through and
stretched between the two holes in the cover provided for
that purpose. Closing the lid operates a lever (g) which
raises the dial to protect the compass from injury when not
in use. To lower the dial push clamp (g) forward with the
thumb. A second glass protects the face of the dial when
the lid is raised. On it is painted a luminous movable index
which is used to set angles from the line of sight or north
point. This glass can be revolved by unlocking the set screw
(h) and turning the corrugated brass ring so that the mova-
ble index points at any angle from the line of sight. It can
then be set at this angle by tightening the set screw (h). A
rubber washer is fixed to the bottom of the case to prevent
slipping when laid on smooth objects. The compass is carried
in a stout leather case with a belt loop. The outside of the
brass case is marked with two scales, one to read azimuths,
and the other to read compass directions. Figure 62 shows
one use of this outside scale.

Ill A— 114

Luminous mark set
by night marching
scale

Compass so held that
luminous arrows on dial
point to luminous mark.

a. Eyepiece

b. Compass card or dial (with

luminous arrow) .

c. Moveable index mark on crystal

(luminous)

d. Hinged cover

1.0. 3503

e. Holding ring

f. Etched front sight cover

g. Clamping knob for compass card

h. Index locking screw

i . Dampening plunger

j-j' Luminous marks on cover

Figure 61. — Prismatic compass.

Ill A— 115

AZIMUTH. HE HENCE ARRIVES
AT A KNOWN POINT OUTSIDE
THE ENEMY'S POSITION. HE
LIES HERE UNTIL SOUNDS
INDICATE POSITION OF ONE

OF THE ENEMY OUTGUARDS.

ENEMY OUTGUARD

WITH COVER DOWN AS SHOWN
SCOUT SIGHTS IN DIRECTION OF
SOUND.TURNS LUMINOUS INDEX

ON THE ROTATING RING—

TO POINT OVER NORTH END

OF ARROW. AZIMUTH IS

NOW RECORDED AND MAY

SCALE.

SCOUT ALSO ESTIMATES

DISTANCE TO SOUND.

RD 3503

Figure 62. — Use of compass dial.

Ill A— 116

The compass is affected by presence of iron, steel, or
electricity, and will not give accurate readings near an auto-
mobile, tank, fieldpiece, machine gun, or power line. A steel
helmet, rifle, or pistol on the person of the observer may in-
fluence the needle and make readings inaccurate.

(2) Lensatic. — The lensatic compass functions in
much the same manner as the prismatic compass. The hinged
eyepiece is a narrow piece of metal containing a magnifying
lens in the larger circular opening. When the eyepiece is
tilted so that it is aimed at the forward part of the compass
face, the observer is able to see both the scale and a distant
point at the same time. It should be noted that the face has
two scales, the outer one showing mils, and the inner one
showing degrees. The compass is made of light aluminum
and is designed so that it may be carried in a pocket.

b. Measuring azimuth with prismatic compass. — To

read the azimuth to any point proceed as follows (fig. 61) :

(1) Raise cover (d) and eyepiece (a) vertically,
and lower needle dial at (g).

(2) Hold compass horizontally in front of the eye
and pointing in the direction of object, azimuth of which is
desired. In doing this utilize every possible means for hold-
ing compass and eye steady. Methods used are somewhat
similar to those used for sighting a rifle. A good method is
to rest head, wrist, and body against a good substantial tree
or other nonmetallic object. A prone or sitting position simi-
lar to that assumed for firing a rifle is also suitable. The dial
may be dampened by operating the plunger (i) with index
finger of left hand.

(3) Sighting through slot in eyepiece, line up
object with etched line (f) in cover. Hold compass steady
until dial comes to rest. Read azimuth indicated on dial as
seen through eyepiece. This will be the magnetic azimuth of
the line from observer to object.

c. Marching by compass. — (1) Day. — Often troops
are ordered either to march or attack cross country according
to given azimuths. Such troops might include patrols or indi-
viduals on scouting or messenger missions. Patrol leaders or
unit commander may compute from a map azimuths or various
legs of their routes to prevent getting lost. Map azimuths
must then be converted to magnetic azimuths before they can
be used with the compass. Having determined this mag-
it until required azimuth is read on the dial. He then sights
along axis of the compass as described in b (3) above and
selects a house, tree, rock, or other easily recognizable feature
of the landscape in this line of sight. He then marches toward
this selected feature until he reaches it or loses sight of it.
He then takes another sight as described above and selects a

III A— 117

new feature. This is repeated until he reaches his destina-
tion. Note that the compass is used to select successive fea-
tures on the line of march and is not used when actually
marching.

(2) Night. — For marching at night, movable in-
dex (c) luminous marks (j-j') on inside of cover, and azimuth
scale on the outside of case are used (fig. 61). To march on
given azimuth at night, set movable index at desired azimuth,
rotate compass until needle points at movable index, and
then select some feature on the skyline that is on the axis of
the compass. March toward this selected feature. The
axis of the compass can be determined by means of the lumi-
nous marks (j-j')- Setting the compass must be done in the
light, usually by flashlight, screened from observation. On
very dark nights where the skyline is not visible, it may be
necessary to send one man ahead to the limit of visibility,
line him up on desired azimuth, and walk toward him, repeat-
ing this as often as is necessary.

ill A— 118

SECTION 10

AERIAL PHOTOGRAPHS

72. General. — a. Importance. — Aerial photographs are
used for many different purposes in connection with military-
operations. In this manual they are considered primarily
in conjunction with or as substitutes for topographic maps.
The ideal situation is to have an accurate topographical map
and a recent aerial photograph of the same area. During
the first few days or even weeks in a new theater of operations
there is a great possibility that the only up-to-date infor-
mation of the terrain available would be that obtained from
aerial photographs. They would be used in determining dis-
tances and directions, and in selecting routes in much the
same manner as ordinary topographic maps.

b. Types.- — (1) Vertical photographs are those made
when axis of the camera is kept as nearly vertical as possible.

(2) Oblique photographs are those made when
axis of the camera is deliberately tipped from the vertical.

(3) Composite aerial photographs are made with
cameras having one principal lens and two or more surround-
ing and oblique lenses. The several resulting photographs
are corrected or transformed in printing so as to permit
assembly as verticals with the same scale.

c. Data on aerial photographs. — (1) As aids in read-
ing and use, aerial photographs to be used individually will
have the following information on the back when issued by
the Navy or Marine Corps.

(a) A Bureau of Aeronautics number, as
M.A.S.Q 216 (Marine Air Station, Quantico #216)

(b) Date.
Unit— as, (Marine Corps Air Station,

Quantico, Va.)
formation)

(c)
(d)

Subject — (plus additional pertinent in-

(1') Altitude flown.

(20 Lens focal length.

(30 Film and filter.

(40 Type camera.

(50 Time of flight.

Ill A— 119

(2) Army Air Corps photos will have information
along the black strip at the bottom reading from left to right,
as follows :

(a) An arrow one-half inch in length in the
lower left hand corner of the negative indicating north, with
letter N superimposed over center of shaft.

NOTE: Some photos may show a similar arrow without letter "N"
superimposed over the shaft. This is a flight direction arrow,
shown in conjunction with the lower left corner neat line,
and is not to be confused with a north direction.

(b) Name of locality or nearest locality.

(c) Approximate military grid coordinates
of center of photograph.

(d) Scale of photograph expressed as a rep-
resentative fraction in case of a vertical, altitude above
ground in feet and focal length of camera in case of an
oblique.

(e) Hour.

(f) Date arranged in the following order:
day, in figures; month, in letters; and year, in figures.

(h) Serial number of negative. In addition
to a north point, the following is the legend on a vertical:
Saranac, N. Y.— (321-437)— 1:20,000—
(2:00 P. M.) — (24-Aug-40)— 97th-M5. (See fig. 68.)

(3) Mosaics and wide coverage photographs may
have in addition to that listed above the following information :

(a) Marginal information similar to that
shown on map legends.

(b) Some system of grids, preferably the
atlas grid described in paragraph 77.

(c) Names of important features such as
town, streams, mountains, highways, etc.

Ill A— 120

Imaginory line passing through axis of camera and parallel
\ to earth.

Oblique photograph,
(broken lines)

Shape of area covered
by oblique photograph.

Figure 63. — Relative shape of area covered by oblique photograph com-
pared to photograph itself.

73. Oblique. — Normally in making obliques the photographs
are taken over the side of the cockpit with the camera
intentionally tilted at an angle which will vary according to
the mission, but is usually about 30° below the horizontal
as shown in figure 63. This procedure gives what is known
as a low oblique (fig. 64). Obliques which include the
horizon are termed high obliques. Figure 63 also shows the
relative shape of the area covered by an oblique photograph
as compared to the photograph itself. Note the actual photo-
graph is a rectangular print whereas the area covered by the
photograph has the shape of a trapezoid. Distances on oblique
photographs cannot be scaled accurately. However, since the
oblique picture is taken from a viewpoint similar to that of an
observer on a high hill, terrain features have a more normal
appearance than they do in a vertical; this characteristic
makes them more useful for the study of hills, valleys, build-
ings, roads, etc. They can also be used to accompany opera-

Ill A— 121

Ill A— 128

Figure 64— Low oblique

Figure 64. — Low oblique.

tions or field orders, to show the line of departure, routes from
bivouac to assault position, assembly positions, boundaries be-
tween units, objectives, and information of the enemy.

74. V e r t i c a 1. — Vertical photographs are usually taken
through an opening in the floor of the airplane cockpit, with
the optical axis of the camera perpendicular to the surface of
the earth. Each photograph covers a comparatively small
ground area and shows the area somewhat as it would appear
on a detailed map or sketch of similar scale. Figure 65 shows
a vertical of the area covered by the oblique in figure 64.
Note the difference in appearance of objects which appear on
both photographs. Note particularly the house at (1), high-
way underpass at (2), tree and tennis court at (3), field at (4),
and orchard at (5). Learning to read a vertical photograph is
similar to learning to read a map. It consists in being able to
recognize familiar objects on the landscape from their appear-
ance on the photograph, to orient the photograph, to determine
its scale, and to determine distance and direction. A photo-
graph, however, is not as easy to read as a map. Important
features on a map are emphasized and always are shown in the
same manner. On a photograph important features such as
portant than a great amount of unimportant detail, or may be
completely hidden by trees or shadows. Dissimilar objects
same objects may appear to be different on various photo-
graphs or even on different parts of the same photograph. Also,
a single vertical photograph, unlike a topographic map, con-
tains no definite information of ground forms and elevations.
Hills, ridges, and depressions are difficult to visualize unless
an analysis of the drainage system within the area is made.
Even when this is done relative elevations are not apparent
on the photograph. On the other hand, an aerial photograph
is very valuable for the reasons that it —

a. Possesses in pictorial form a wealth of detail which
no map can equal.

b. Can be prepared for use in a short time, much
quicker than making a new map.

c. Is up to date.

d. Can be made of any area, even those inaccessible
to ground mapping parties.

75. Identifying Terrain Features. — a. Identifying features
of terrain on photographs requires a certain amount of prac-
tice which is best gained by actually comparing the photograph
with the ground. When this is not possible, the next best
method is to compare photographs with a good map of the

III A— 125

same area. Actual identification of objects on an aerial
photograph or on a mosaic is effected through one or more
of the following means:

(1) Shape of object.

(2) Its tone, or relative colors from white through
various shades of grey to black.

(4) Apparent or relative size.

(5) Relative location or environment.

b. In identifying features on a vertical photograph,
always hold the picture so the shadows are falling toward you.
Figure 66 shows several ground features numbered to corre-
spond to the numbers of the subparagraphs below containing
their description ; when reading the description, look at Figure
66 and note how reasons given for each identification apply.

(1) Plowed field looks light in the photograph
because it reflects a relatively large amount of light.

(2) Meadow looks darker largely due to the
texture than the field. The difference between the meadow
and the field is similar to the difference between satin and
plush velvet. Although both are the same color, the plush
looks darker due to the shadows of the hairs which stand
erect, but it can be made to look lighter when smoothed
down.

(3) In this photograph, the highway bridge looks
lighter than the water. It can be identified by its size, shape
and its shadow on the stream.

(4) Building can be identified by its size, shape,
difference in appearance of the two roof slopes, and by its

(5) Woods appear relatively dark because of deep
shadows of the trees. They have much texture and reflect
little light.

(6) A stream can be identified by its meandering
course. Even through open fields some trees or bushes
usually grow along its banks. In a dense wood it will appear
as a thinning out of the surrounding growth. The water
looks very light or dark, depending upon the relative positions
of sun, camera, and water.

Ill A— 126

rd mmti)

.&&,, -■■;:■<■■>;-,

III A— 127

3k-

^

in

Ifcl !■ ifc (■■■!! Ill

ST

J^frfl X ''l

"^ ^p?

-. ^Bam 9

I«|P^

SnL— ^

Figure 65. — Vertical photograph.

*%

^mmsB&. ^* '

III A— 129

Figure 66.— Identifying Terrain Features.

Figure 66. — Identifying Terrain Features.

(7) Fence lines are identified by difference in
texture between fields they separate and usually look dark
in the photograph because of shadows- of bushes growing
along them.

(8) Roads are identified by their straight lines,
uniform width and the fact that their surfaces are usually
smooth and reflect much light. (Modern open asphalt texture
surfaces will appear darker than other road surfaces.)

(9) Trails are also light but are more variable
and narrow in width and more crooked than roads.

have more fills and cuts, and are straighter, and darker in

(11) Orchard is identified by its shape and by the
straight and regular rows of trees. Shadows of equal length
show the trees are all about the same height.

(12) Mud flats along the stream look darker than
the water and have lighter spots in them due to pools of
water.

(13) Cluster of buildings shows this a village.

c. A careful study of Figure 66 combined with a study
of Figures 64 and 65 should make the student reasonably
proficient in interpreting aerial photographs. It should be
remembered that the pictorial effect of vertical aerial photo-
graphs is influenced by shadow. In order that this effect
will aid rather than hinder the student, he should place the
photograph on a table between himself and a lamp, window,
or other source of light, shifting it to avoid the glare from
its surface and so that shadows on the photograph fall toward
him. In this position objects will have their normal appear-
ance. If the photograph is reversed, that is, placed so that
the shadows fall away from the student, actual hollows may
appear as hills and trees as holes in the ground.

76. Orientation. — a. With map. — (1) When the -photo-
graph is used in conjunction with a map it should be oriented
with a map. Maps are printed with the north of the map
at the top and all lettering, grids, etc., are added on that
basis. However, no attempt is made to take photographs to
fit this scheme. Photographs may be received without any
lettering or direction for orientation. Consequently it may
be necessary to study the photograph and identify objects
to use in orienting it. When objects shown on the map are
found on the photograph it is a simple matter to orient the
photograph with respect to the map. Road systems and
streams are useful for this purpose. A magnetic north line
should then be drawn on the photograph parallel to that on
the map.

Ill A— 131

a
So

O

o

-

III A— 132

(2) Another method of drawing the magnetic
north line on a photograph is to select two points on the photo
that can also be easily identified on the map. The points
should be fairly far apart, and line joining them should pass
close to the center of the photograph (points A and B, fig.
66). Measure on map azimuth of line joining these points.
Convert this azimuth to magnetic azimuth. Assume the
magnetic azimuth of AB on the map to be 35°. Lay protractor
on the photograph (fig. 67 with center of protractor at A
and line AB cutting the 35° reading. The base line of the
protractor is now lying on magnetic north and south line
with north toward the 0° reading. A line with N arrow is
drawn parallel to this where desired on the photograph.

b. With ground.— A photograph may be oriented with
the ground by placing some well-defined line as a road on the
photograph parallel with the same line visible on the ground.
This is similar to the orientation of the map described in
paragraph 67. The same method is used in locating observer's
position on a photograph as is used on a map.

c. By shadow. — There may be times when an observer
in the field finds it impossible to orient a vertical aerial photo-
graph by either of the above two methods. A third method
of rough orientation by use of shadows can be used. In the
northern hemisphere shadows fall to the northwest in the
morning and to the northeast in the afternoon. Assume the
photograph is taken between the usual hours for aerial photo-
graphy, that is, 10:00 A. M. to 2:00 P. M. The photograph
is laid on the ground with the shadows pointing slightly west
of north if the photograph was taken in the morning or
slightly east of north if taken in the afternoon. The photo-
graph is then approximately oriented. If the exposure is
before 10:00 a.m. or after 2:00 p.m., the photograph must
be turned west or east of north a correspondingly greater
distance.

77. Atlas Grid. — a. Because of variations in scale, other
inaccuracies, and difficulty of locating grid lines, the military
grid is not used on photographs or uncontrolled photomaps.
The atlas grid is used instead with grid lines always 1.8
inches apart regardless of the scale. With this interval, on
a 1:20,000 photograph the grid lines are about 1,000 yards
apart. The lines are numbered from the bottom up, and
lettered from left to right. Starting at the left edge, the
first line is A, the second B, etc. Therefore, the origin of
coordinates at the lower left-hand corner of the photograph
is (A.0-1.0) (fig. 68). Points can be located accurately by
decimals of the gri,d interval.

b. In the process of reproduction, the edge of a photo-
graph may vary and successive prints may differ. For the
purpose of making accurate measurements, the neat lines,

III A— 133

which are of constant dimensions are considered as the edges
of the photograph. Only the corner ticks of the neat lines are
usually registered on a photograph. Its ticks at the lower
left corner are used as the origin for the Atlas grid. The co-
ordinates of point P (fig. 68) would be written (C.5-4.2).

Figure 68. — Atlas grid and marginal data.

c. Various other special grids may be used on aerial
photographs or maps. They are generally devised and named
for a single operation and generally are based on the atlas
grid. A knowledge of the atlas grid will give a background
to interpret other grid systems.

78. Scale. — Customarily photographs intended to be used
as substitutes for maps will be marked as described in para-
graph 72. However, they may be received without complete
information, as for example, with the scale omitted. In this
case the scale must be determined by some other method.

a. By focal length and altitude. — Generally the focal
length and altitude at exposure will be shown. This informa-
tion would appear in the marginal data as follows : (12"-20,000) .
This means that the picture was taken with a camera focal
length of which was 12 inches and was 20,000 feet above the
ground at time of exposure. By inspection of figure 69 it may

III A— 134

I

NEGATIVE *

LENS

GROUND IA

R.D.3503

H= LENS HEIGHT

Figure 69. — Diagram showing relation of scale, focal length, and
lens height.

be seen that there is a direct relation between the focal length
of the camera, height of the plane, ground distance AB and
corresponding distance ab on the photograph or

f
H

ab
AB

= RF

If the focal length is 1 foot (12 inches) and the altitude of
the plane is 20,000 feet then the scale of the photograph will

be

20,000

or RF = 1 :20,000.

Ill A— 135

If the focal length had been 6 inches, then the scale would

6/12 i/ 2 1

have been or = or RF = 1 :40,000.

20,000 20,000 40,000

Hence the general expression or formula is:

Focal length in feet

RF =

Height of plane in feet

In some cases the altitude is the elevation above sea level, and
not the elevation above the ground. If the average ground
elevation is much above sea level, allowance must be made
for this by reducing the plane's height by the elevation of
the ground. For instance, in the example given just above,
if the ground had been 2,000 feet and the altitude given had
been the elevation above sea level, the RF would have been
actually

V2 1

= or 1 :36,000 instead of 1 :40,000.

20,000-2,000 36,000

b. By comparison with map or ground distance. — The

average scale of the photograph may be computed by com-
parison of the distance between two points on the photograph
with corresponding distance between the same points on the
ground or on a map. For best results the points chosen
should be located on the photograph so that straight lines
joining them pass fairly near to the center and well across
the face of the photograph. If required to find the scale of
the photograph in Figure 66 by comparison with a 1:20,000
map of that area, select two point such as A and B, that are
easily recognizable both on the photograph and on the map.
Measure the distance between them both on the photograph
and on the map. In this case assume the map distance to be 2
inches, which on the ground would be 2 X 20,000 = 40,000 inch-
es, since the scale of the map is 1 : 20,000. The distance between
points A and B on the photograph is 3.8 inches. Since it is
known that the distance on the ground is 40,000 inches then
the RF of the photo is

3 8 1

' = or 1:10,526.

40,000 10,526

Now suppose it is required to find the scale of the photo-
graph in Figure 65 by comparison with a 1 : 10,000 map. Select
two points such as (2) and (6) that can be identified easily
both on the photograph and on the map. Proceed as above
and in this case assume map distance to be .8 inches which

III A— 136

\

would be 8 X 10,000 = 8,000 inches on the ground. The dis-
tance on the photograph is 3.5 inches. Therefore the RF of
the photograph would be

3.5 1

= or 1:2,286.

8,000 2,286

Note that in both examples, points were selected so that
lines connecting them passed close to the center of the picture
and that the points were far apart.

79. Mosaic. — A mosaic consists of several overlapping ver-
tical photographs joined together. When these photographs
are oriented with respect to each other by matching detail
in the overlap or along the border, the result is an uncontrolled
mosaic which gives a good pictorial effect of the ground but
may contain considerable errors in scale and direction. When
the several photographs are oriented by means of points
along the line of flight and adjusted on previously selected
ground points, the result is a controlled mosaic. The con-
trolled mosaic is more accurate and for many purposes is
as useful as a map. When several photographs taken from
a single airplane flight are joined, the result is a strip mosaic.
Strip mosaics are commonly used in the early stages of combat
as they are quickly made and give a fairly accurate repre-
sentation of a more or less extended but narrow section of the
terrain.

80. Photomaps. — A photomap is a single photograph, com-
posite, or mosaic which has been prepared by the addition of
grid, marginal and place-name data, and produced in quantity
by contact printing or lithography. When time for prepara-
tion and available information permit, this data will be in
the same form and as complete as for standard maps. Since
the photomap, however, finds its greatest use in providing
information quickly, quite frequently much of the data usually
found on a map will be missing.

81. Marginal Data. — Marginal data for the reproduced indi-
vidual photograph will be that given in paragraph 72c. Photo-
maps which are made from mosaics and certain wide coverage
photographs may have, in addition, the following information:

a. Marginal information similar to that shown on
maps, such as the graphic scale of yards.

b. Some system of grids, usually the atlas grid.

c. Names of towns, streams, mountains, highways,
and other important features.

82. Care in Use of Photomaps. — Photomap users will make
their own estimates of the reliability of the information
portrayed by examination of the marginal information and
by consideration of the basic materials used in their prepara-

III A— 137

tion. The date of the aerial photography gives an indication
of the probable accuracy of portrayal of cultural features
as they now exist. If the photomap is a simple reproduction
of a single photograph or composite, it will be understood
that the indicated scale is approximate and that over-all scale
errors due to tilt and relief displacements will exist. Photo-
maps from mosaics will be indicated as "controlled" or "uncon-
trolled." Photomaps made from uncontrolled mosaics are
important primarily because of their pictorial value, and should
not be considered as accurate for the determination of dis-
tances and directions. If the area is relatively flat and the
photographs have been taken at fairly constant elevation
with little tilt, even the uncontrolled mosaic will approach
the dimensional and directional accuracy of the best maps. A
photomap from a controlled mosaic may be accepted as reason-
ably accurate for measurement of distances and directions,
despite the fact that image displacements at the junctions
of the individual prints will be apparent. Such photomaps
may be accepted with the same degree of confidence as a first
class planimetric map of the same scale.

83. Aids in Use of Photomaps. — Photomaps reproduced in
quantity by photolithography lose some of the clarity, sharp-
ness, and contrast of the original copy. Even in poor repro-
ductions, however, the principal features of the terrain can
be discerned by careful study and through the application of
general knowledge of terrain characteristics. It will assist
the map reader considerably to trace the drainage system,
accentuating the stream lines with a sharp blue pencil, avoid-
ing, at the same time, the obliteration of essential details. In
the same time, the permanent ridge lines may be traced in
brown lines, thus enabling the map reader to grasp at a glance
the major features of the terrain.

84. Methods of Reproduction.— -Photomaps are reproduced

in quantity by contact printing, by continuous tone litho-
graphy, or by halftone lithography. The contact process
produces the best results, but is much more expensive and
time consuming than lithography. Furthermore, rapid con-
tact printing of large size photomaps requires equipment
which is too bulky for field use. In the continuous tone
lithographic process, much of the contrast of tone which
appears in the original photograph or mosaic is lost. As a
result, many small features become merged into the back-
ground and are difficult or impossible to discern. When the
original photography has been satisfactory, the best results
in quantity reproduction are obtained by halftone photolitho-
graphy. Reading glass examination of a photomap reproduced
by this process will disclose the individual images are made
up of a series of dots, the darker the object, the denser the
dots. Most of the original tone contrast of the photograph is
retained. However, in the halftone process also, some details

ill A— 138

of the landscape such as individual bushes, small houses etc.,
may be too small to create a sufficiently distinct dot pattern to
render them recognizable. Another feature to be observed
in the study of photomaps from mosaics is the variation in tone
and contrast between adjacent photographs used in the prepar-
ation of the mosaic. Because of changes in exposure condi-
tions, as well as variations m printing of individual photo-
graphs, marked differences in the tone of adjacent sections
of the mosaic frequently occur. Such differences in tone should
be recognized readily and should not be misinterpreted as
actual changes in landscape texture.

85. Stereovision. — a. General. — The ordinary photograph,
has a flat appearance, which makes it difficult to distinguish
between hills and valleys. If two overlapping photographs,
known as a stereopair, are viewed either with the naked eyes
or with some type of stereoscopic instrument, the effect of
depth or relief will be seen and ability had to recognize the
actual ground forms. This type of study gives valuable train-
ing in understanding and reading both single vertical photo-
graphs and photomaps. Consequently all military personnel
should learn and practice stereovision. There are several meth-
ods that will assist in acquiring this ability and each individual
should experiment until he finds the method that gives him the
best results. This ability comes very quickly to most; others
will have to use patience and perseverence to obtain it. Experi-
ence with large groups of men reveals that anyone with good
enough eyes to be in military service can acquire the ability to
see stereoscopically. Stereo studies properly done put no strain
on the eyes, and some oculists even prescribe similar exercises
to strengthen the eyes. However, when magnifying spectacles
are used, they should be removed from the eyes before looking
up from the photographs.

b. Anaglyph. — Beginners in stereo studies often have
difficulty in getting the effect of relief by means of aerial
photographs. A simple method of illustrating stereovision
is by means of the anaglyph. The anaglyph consists of two
different photographs of the same area printed on the same
sheet but slightly offset. One is printed in red and the other
in blue or green. Relief can be seen when the anaglyph is
viewed through a pair of colored spectacles. If the spectacles
are reversed or the print is turned upside down, the relief is
reversed and ridges will appear as valleys and valleys as
ridges. The anaglyph has no practical military value and
is used as a quick aid to beginners to illustrate the effects
to be obtained by practice in stereovision.

Ill A— 139

SECTION 11
HYDROGRAPHIC CHARTS

86. Definition. — The hydrographic chart is a conventional
representation of a portion of the earth's surface, chiefly of
that portion which is covered by water, or that on which land
and water meet to form the shore line. In the conduct of
landings, Marine Corps personnel will be concerned with the
latter class only.

87. Sources From Which Charts Are Obtained. — There are
three sources from which charts may be obtained in the
United States : the Coast and Geodetic Survey of the Depart-
ment of Commerce, which publishes, from its surveys of the
coast line, charts suited to the purpose of navigation and
defense; the Hydrographic Office of the Navy Department,
which has charge of the duplication of charts issued by foreign
governments and the preparation and publication of charts of
coasts not under the jurisdiction of the United States; and the
Corps of Engineers, U.S. Army which prepares and issues
charts of the Great Lakes.

88. Types. — a. Generally speaking, there are four classes
of charts, each made to its own particular scale, and intended
for use in its own peculiar way.

(1) The first, known as the sailing chart, embraces
long stretches of coast line or large reaches of water. This
class is of interest to navigators of overseas craft only.

(2) The second, known as general charts of the
coast, are made to a scale three times as great as the first
class, and the charts themselves show limited, but still large
areas, such as the Gulf of Maine, the Puget Sound Area,
Chesapeake Bay, etc. They are intended for coastwise navi-
gation, chiefly by the use of landmarks, buoys or soundings,
and are of little use in landing operations, but may- be em-
ployed when more detailed charts are not available.

(3) The third class, known as coast charts, are
constructed on a normal scale of one inch to the nautical mile,
or one inch to one and one-seventh land miles, which is about
five times the scale of the second class. This class shows the
details necessary for close coastwise navigation, for entering
bays and harbors, and for navigating inland waterways.

(4) The fourth class embraces harbor charts,
which are constructed on large scales, intended to meet the
needs of local navigation. No definite scale is prescribed, as
the scale used in each case must be adequate to afford an
accurate and useful representation of the waters and coast line
to be encountered. However, it has been found that, as a
general rule, scales varying from 1 :40,000 to 1 :20,000 are to
be found on the charts.

Ill A— 141

b. The last two classes of charts are most suited to the
needs of Marine Corps personnel in landing operations, as
they show in sufficient detail the aids to navigation, bottom,
channel, and shore line conditions to enable subordinate com-
manders to pick up suitable routes to the beach as well as to
pursue their operations for at least one thousand yards inland.
Charts of these two classes will form the basis for study.

c. While the scales given above are standard for charts
of the coast line of the United States and possessions, these
scales may not apply to foreign charts or copies thereof. How-
ever, in all cases, as in the case of topographic maps, a scale
of some sort is usually to be found on the chart, which scale
should be verified as soon as possible by the prospective user.

89. Correction. — The prospective user should also examine
the chart with a view to ascertaining the date of its manu-
facture or issue. In many instances, especially in the case
of river mouths or harbor entrances, there is likely to be a
change of a drastic nature in the condition of bottom, channel,
or shore line, and a chart of some age, which has not been
corrected up to date, is likely to prove more dangerous than
no chart at all. The date of manufacture and/or of issue is
usually printed or stamped prominently on the face of the
data shown by the original chart a notation to this effect
appears near the date of issue.

90. Conventional Signs. — a. The conventional signs, ab-
breviations and systems of lettering for use on charts are
found in FM. 21-30 and column 4 and 5 of the sheet of stand-
ard symbols and in Correspondence School text "Military
Abbreviations and Symbols." Of particular importance under
this heading are the abbreviations relating to bottoms and
the general abbreviations, since it is of interest to landing
personnel to know what character of bottom they will en-
counter in landing men and materiel without wharf facilities.

b. With regard to notations as to depth, it is standard
practice to use both depth curves and numbers to show depth
in feet or fathoms, the depth shown being taken at mean low
water. The showing of depths in fathoms is exceptional in
coast or harbor charts, depths on these being shown in feet.
In any case an explanation of the unit used usually appears
in the legend.

c. Works of man or terrain features on shore are shown
on charts in the same manner in which they are shown on
topographical maps, except that, where the height or promi-
nence of an object makes it a good landmark, it is customary
to make a note of the fact, giving characteristics of the object,
its height and, sometimes, width. In British Admiralty charts.

III A— 142

the practice exists of putting on the border of the chart a
panorama which shows the general appearance of the coast
line or harbor entrance from seaward. -

In general, also, in delineating shore characteristics no
colors are used, conventional signs being in black on a buff or
cream-colored background.

d. In some cases, contours or hachures are used on
the landward portions of charts. The normal contour interval
is twenty feet.

e. No grid system is ordinarily put on hydrographic
charts.

f . With regard to direction, all charts issued by United
States authorities have, at as frequent intervals as possible,
a compass card graduated from zero to three hundred and
sixty degrees in the divisions of one degree. The zero of this
card indicates true north. Inside this card is a second card,
graduated according to the points of the compass, whose zero
points to magnetic north ; thus, the declination or as it is called
in nautical parlance, the variation, is shown graphically.
There is also given a notation showing the annual change of
variation, usually in terms of increase or decrease.

g. Bottom conditions appear in the form of abbrevia-
tions, i.e., g for gravel, hrd. for hard, sft. for soft, etc. As all
charts carry a definition of the abbreviations used in the par-
ticular chart, and as a complete list of these is also to be found
on the "Sheet of Standard Symbols" their interpretation should
be simple.

h. Aids to navigation are of comparatively minor
importance to troops engaged in landing operations. However,
it should be remembered that the universal rule for the placing
of channel buoys is that red buoys are placed so that they will
be on the right of the channel on entering it, or on moving
upstream, and black buoys on the left. Also, for the benefit
of students who may be unfamiliar with nautical phraseology,
it is thought well to give here a definition of the most com-
monly used types of buoys. A nun buoy is made in the form
of a cone, and is anchored with its apex uppermost, a can buoy
looks exactly like its name, and is anchored with its long axis
vertical; a spar buoy consists of a single spar, about twelve
inches in diameter, anchored so that it floats in a vertical posi-
tion with about ten feet showing above the water. Inciden-
tally, as all anchored buoys must swing with the tide or current
to some extent, these can be used to give an instant indication
of the direction of the flow.

In connection with the identification of can buoys (see
preceding page) there is a possibility of confusing them with
a certain type of mooring buoy. The latter is usually a large
cylinder with about twice the diameter of a standard can buoy,
usually painted black, and with an eyelet bolt or short length

III A— 143

of chain thru which to moor, fastened to its uppermost
surface. Also, it is invariably placed outside the channel, if

91. Additional Publications. — There are certain other publi-
cations which may be of value in landing or base defense
operations, altho the information contained in them is mainly
included, where applicable, in charts or the legends thereof.
Two of these are of particular value. The first is the Light
List. It is published annually by the Department of Com-
merce, and contains information as to the name, character,
color, and period of light of each light within the area along
the Atlantic Seaboard and Gulf Coast. Similar lists are pub-
lished by many foreign governments for the coast lines under
their control or cognizance. Second, and more important, are
the Tide Tables, published annually by the Department of
Commerce in three editions. The first, known as the General
Tide Tables, gives information about the tides in all of the
more important ports in the world. The second is the Atlantic
Coast Tide Tables, for eastern North America; and the third
is the Pacific Coast Tide Tables for Western North America,
Eastern Asia, the island groups included between these coasts
and a few others to the southward. All of these give, for the
locality in question, the time of every high and low water for
every day in the year, and the height of each of these above
mean low water. Altho the possession of these tables is
desirable for officers engaged in landing operations, and altho
familiarity with their use and interpretation is of value to
all persons engaged in such operations, their possession by
the individual is not essential, as they are issued to the cruis-
ing vessels in the Navy.

92. Factor to be Considered in Making a Chart Study. —

a. Maps of land areas which border on water do not
furnish sufficient information as to the places along the shore
line at which landings can actually be made. On the other
hand, hydrographic charts do not always give, in sufficient
detail, information as to the nature and character of ground
in the immediate vicinity of the shore line. Where practicable,
the two types should be used in conjunction with each other.
To supplement the information gained from charts a personal
reconnaissance of the shore line from seaward should be made
wherever possible, but where such reconnaissance is not possi-
ble, charts, or charts and maps of the areas involved should
be studied with a view of obtaining information necessary to
effect a safe and rapid landing.

b. In making a map, chart, or map-and-chart recon-
naissance, the types of boats to be used should be considered
in conjunction with the characteristics of the shore line. In
considering the types of boats, attention must be paid to the
following features:

(1) Draft, both loaded and empty.

Ill A— 144

(2) Speed.

(3) Backing power.

(4) Rigidity of construction and ability to with-
stand shock and abrasion (seaworthiness).

(5) Motive power.

(6) Manner in which propeller (s) and rudder are
attached.

(7) Type of construction (e.g., whether with flat
or keeled bottom, etc.).

c. Having in mind the type of boat available, a study
of the shore line as depicted should be made. The items to
be noted in making such a reconnaissance should include:

(1) Length, in yards, of stretches of beach suit-
able for landing.

(2) Distance from shore line (at mean low water)
at which the types of boats available may be expected to
ground.

(3) Character of water at shore line ; whether surf
or smooth.

(4) Character of bottom between grounding point
and water's edge. This feature is particularly important, as
it must be remembered that troops making the landing must
traverse this area on foot, carrying their personal equipment
and arms, and in some cases, moving light wheeled vehicles.

(5) Underwater obstacles, such as reefs, bars, iso-
lated rocks, etc., which would endanger boats of the type
available.

(6) Character of soil at landing beaches.

(7) Location and character of vegetation nearest
to shore line.

(8) Prevailing winds at landing beaches.

(9) Suitability of beach and vicinity for landing
seaplanes, if same are present.

(10) Times of maximum high water and of mini-
mum low water.

d. With regard to adjacent terrain the following items
should be noted:

(1) Points inland from which infantry- weapon fire
can be placed on the selected beaches.

(2) Most advantageous routes from the beach, by
which towns or other strategic points in the vicinity of the
beach can be reached.

(3) Points along the route or routes mentioned
above at which resistance is most likely to be encountered.

(4) Points offering good observation to the land-
ing force in its advance from the shore line.

Ill A— 145

(5) Points nearest the beach at which measures
may be taken to interfere with or divert to the use of landing
force (a) hostile traffic, (b) local lines of water supply, (c)
local public utilities, such as railways, electric-transmission
lines, telegraph or telephone lines, gas lines, fuel supply, etc.

(6) Location of possible source of fresh water
(other than the above) in the vicinity.

93. Limitations. — Hydrographic charts, being primarily de-
vantages when employed as military maps.

a. Mercator Projection. — The Mercator projection is
normally used on hydrographic charts. This projection assumes
the meridians of longitude to be parallel and does not take into
consideration their convergence at the poles. Hence, the distor-
tion of a Mercator projected map or chart is zero at the equator
and infinity at the poles. This greatly facilitates the marking
off of latitude and longitude with dividers on these charts, but
also greatly distorts earth masses and distances. In the ab-
sence of an overprinted military grid, the lines of latitude and
longitude can be used in conjunction with an improvised co-
ordinate square to give geographic coordinates.

b. Distances. — Distances are normally expressed in
nautical miles. A nautical mile equals one minute of latitude
which equals 6080.20 feet or 1.15 statute miles. The term knot
as used by the Navy and by Marine aviation is the speed of one
nautical mile per hour. Nautical miles and knots may be readily
converted to statute miles by multiplying by 1.15. To convert
statute miles to nautical miles, multiply by .87.

Ill A— 146

SECTION 12

FOREIGN MAPS

94. General. — a. The basic principles of map reading
apply to all maps, foreign and domestic. If the soldier
is capable of applying these fundamentals intelligently to
maps of American design he will require no special or inten-
sive instruction to enable him to read maps from other sources.
Maps which will be used in many theaters will have been copied
either by us or our allies from foreign maps. Intelligent use
of these maps involves not only the mechanical and technical
steps of map reading, but also the ability to evaluate the accu-
racy and limitations of the map information. Europe is the
most completely mapped of all the continents. A fair propor-
tion of North America also has been adequately surveyed, but
the map coverage of the rest of the world leaves much to be
desired both in extent and accuracy.

Maps employed in the early phases of many operations
will undoubtedly leave much to be desired. As the operation
progresses the inaccuracies must be corrected and the inade-
quacies supplemented by aerial photographs and personal
reconnaissance. All ranks and services must be impressed
with the importance of reporting map errors and omissions.

b. Sources. — (1) British. — The best world map cover-
age available to us is that offered by the Geographical Section
of the British War Office and the Survey Directorates of the
Commonwealth and Colonial governments. Since 1940, the
British mapping policy has been the direct utilization of exist-
ing maps of foreign areas without change of sheet lines or
characteristics. First editions will be direct copies, frequently
in continuous tone or half-tone, with no change from the
original other than legend translation and the addition of a
grid. Later editions will contain such revisions and standard-
izations as are possible.

(2) French. — French maps have the reputation of
being both accurate and clear. Their colonial possessions have
been mapped extensively. At the start of the present conflict
the best maps of the northern two-thirds of Africa were
French.

(3) Dutch. — Netherlands maps are of high stand-
ard, detailed, and of good clarity. Their maps of the Nether-
lands East Indies are excellent. Belgian maps are similar to
the Netherlands.

(4) Russian. — Although difficult to obtain until re-
cently, Russian maps have excellent draftsmanship and are
apparently very accurate. Symbols are often complex and town
symbols are keyed to population. In the Siberian areas roads
and trails are shown in terms of summer or winter use.

Ill A— 147

(5) Scandinavian. — Danish, Norwegian, Swedish
and Finnish maps resemble each other closely. The maps are
excellent, but make little use of color.

(6) German. — As might be expected, German maps
are extremely detailed and accurate, but an overabundance of
detail sometimes destroys the clarity of their maps.

(7) Italian. — The Italians have done little with
mapping with the exception of North Africa where they have
produced good maps of their own colonies including the hith-
erto little-known Ethiopia.

(8) Japanese. — Japanese map standards vary from
poor to excellent. They are very often inconsistent, particu-
larly in the Anglicized spelling of place names.

c. Marginal information.— An analysis of the marginal
data is even more important when dealing with foreign maps
than when working with domestic maps.

(1) Authority. — The reliability of a map is largely
dependent on the organization that issued it and the purpose
for which it was made. Governmental agencies are more reli-
able than commercial firms; general purpose maps are more
maps.

(2) Dates.— Maps are only reliable as of the dates
of original survey and subsequent revision. Remember that re-
vision does not necessarily mean a complete modernization of
a map.

(3) Conventional signs and symbols.— F o r e i g n
signs or symbols whose meanings are not obvious will be shown
on the margins of the map.

(4) Scale. — In general, the larger the scale, the
more accurate the map. There are exceptions to this rule how-
ever. "Blow-ups" or enlargements, for instance, can be no more
accurate than the smaller scale map from which they have been
enlarged. "Blow-ups" can generally be identified by the rela-
tive coarseness of composition.

d. Scales and distance. — It is common among all na-
tions and on all maps to show the scale of the map as a repre-
sentative fraction or RF. The unit of measure employed by the
nation does not affect this relationship, whether it be the cho
of the Japanese, the metre of the French, or the mile of the
English. If the unit of measure employed on the map is in-
convenient or unfamiliar to the user, a graphic scale reading
to the desired unit may be readily constructed once the RF is
known.

Most maps which do not show miles will at least show
the metric system. Distance expressed in kilometers can be
converted into miles by multiplying by % or, if a more exact
conversion is desired, by 0.62. For a rough approximation of

III A— 148

the number of yards, multiply the number of meters by 1.1,
or for a more exact determination, by 1.094.

In the event that the contour interval is stated in terms
of meters, this may be converted to feet by multiplying by 3.3,
or more exactly by 3.282. In preparing profile and visibility
diagrams, however, it is not necessary to convert to the usual
English or American units, as the profile produced will have
the same outline regardless of the selected unit.

95. British Grid System. — Most of the foreign maps which
come through British channels have, as an integral part or as
an overprint, the British Military Grid System. This grid
system has the property of being adaptable for accurate sur-
veying without making various grid north corrections such
as are necessary with the United States Military Grid. This
property is obtained by keeping the areas rather small and also
relatively long and slender with the longer axis of the area
being in the direction either of a parallel or meridian. The gen-
eral shape of a country, continent, or other area to be gridded
usually lends itself to a subdivision in one direction or the
other. For example, Netherlands East Indies is easily divided
into long, slender areas running east and west, while East
China is more readily divided into areas running north or
south.

Each area is named as a zone or belt, for example,
Netherlands East Indies Zone of Australia Belt # 5. All
British Grids are printed in a fixed color throughout any cer-
tain zone, the colors for the series of zones being so arranged
that no two adjacent zones will be the same color. There is no
overlap between grid zones.

A grid zone is ordinarily divided into squares of 500 KM
on a side. Each basic square is assigned a letter, the letters
being alphabetical, reading from left to right and down within
a zone, omitting the letter "I." Each 500 KM square is fur-
ther divided into 100 KM squares, each of which is designated
by a letter arranged in the same order as the 500 KM square
letters. Thus, a 100 KM square of a zone may be identified by
two letters, the first of which represents the 500 KM square,
and the second the 100 KM square. Some zones are so long it
becomes necessary to repeat the series of 500 KM squares. In
this case, more than one 100 KM square will be assigned the
same letter. Other zones are so small that neither the 500 KM
or 100 KM squares appear ; hence, no letters will be used in the
grid reference.

On maps of scale 1:250,000 to 1:500,000, the letters
identifying the 500 KM square and the 100 KM square are both
shown on the face of the map. Ordinarily, on maps of scales
1:250,000 and larger, only the 100 KM square letters are
shown, although the letter identification of the 500 KM square
may appear in the grid index diagram on the margin of the
map.

HI A— 149

The spacing of the grid lines is controlled by the scale
of the map. On maps of scales 1 : 20,000 to 1 : 100,000, the grids
are spaced at 1,000 meters and on maps of smaller scales they
are spaced at 10,000 meters. In a few cases, grids on the
1:100,000 scale map will be spaced at 10,000 meters.

To write coordinates :

a. Write the 500 KM square letter.

b. Write the 100 KM square letter. If all pertinent
letters are not shown, it may be necessary to sketch out the
basic square arrangement (fig. 70) to be sure that the proper
letters are applied.

c. Write the east-west coordinates from the lower left
corner of the appropriate grid square, estimating or measur-
ing to the smallest reading desired.

d. Write the north-south coordinates in the same man-
ner, without a hyphen or dash between the two coordinates.
(READ RIGHT UP applies on the British grid just as on that

of the U.S.)

e. Always omit the small numbers which precede the
large grid numbers in the margin.

Figure 70 shows how a map might have British grid
lines placed on it. The letters are always arranged in the same
order, no matter whether the squares are 100 KM or 500 KM.
Every letter in the alphabet is used except the letter "I." The
100 KM square "R" of the 500 KM square "G" is designated
as (G)R. It may be further divided into tenths and hun-
dredths. A point that is 39 KM right of the southwest corner
of this square and 63 KM above the southwest corner is desig-
nated as (G)R3963. If two digits are used in reading right,
two must be used in reading up ; if three are used in reading
right, three must be used in reading up. For example, right
31, up 285 must be written 031285 in order to be understood
which figures mean right and which mean up. One must know
the arrangement of the letters to find the 100 KM square.

Ill A— 150

A

L

B

C

D

K

A

L

B

M

++

D

K

A

L

E
K

Q

U

Q

R

U

Q

U

V

w

X

Y

V

W

X

Y

V

w

X

Y

A

B

D

B

D

A

B

D

++

K

K

H

K

M

U

L

L

VI

U.

Q

R

T

U

Q

U

Q

=*

T

U

V

w

X

Y

V

w

X

Y

V

w

X

Y

B

D

A

m

A

PS,

D

K.

n

U

K

K

K

Figure 70.

96. French Geographic Grid. — French maps show a dif-
ferent geographic grid than the English and American.
The French system bases its grid on a prime meridian estab-
lished as passing through the observatory at Paris. Instead
of using degrees as a unit of angular measure, the French di-
vide their circle into 400 grades* (written 35G, 259G, 365G,
etc.) . Each^grade is subdivided into 100 minutes and each min-
ute further divided into 100 seconds. One grade equals .9
degree, so conversions from one system to the other may be
easily calculated.

Ill A— 151

Following are original Japanese Symbols that would
appear on an original Japanese map.

NOTE: Many of their symbols bear characteristics similar to our
standard symbols, some indicating similar objects while others
indicate entirely different objects.

Factory O

Water Wheel or Mill _ _s_

Generating Plant V

Shrine TT Nipa ~ -** ■**■

Temple re

Mi, >"* >*

Pagoda . m Tropical Grass _. .0//. *\ u »* u '

A ^ >.

Statue . l

iL JL JL JL

Shipyard 8L> Irrigated Rice __> - - -

Field il il iL jl

School X ' " " "

yj KJ O O

Control Point A Orchard 6 , A . 6 . 6 ,

o o o o

6 6 6 6
Bench Mark

•r • t • T • T
Tomb M Bamboo . - -,~ T

Mine ^C

Lighthouse ^ Vineyard ^ ^ ^ <£

Boat Anchorage <J*

Small Boat Anchorage _&

Prison X

Figure 71. — Japanese Map Symbols.

Ill A— 152

I

The Following Publications may be Obtained

from the Correspondence School upon Request by any

Officer of the Marine Corps

Title

Volume

II

Artillery

XXXIII

Combat in Woods

XXXIX

D

XLV

A

Defensive Combat of Small Infantry Units

X

Description of Marine Corps Artillery,

Weapons and Ammunition

XXXIII

Part 3

Elementary Combat Intelligence

XLI

Employment of Artillery by the Infantry

Commander

XXXIII

Part 5

Estimate of Situation and Operation Plans

and orders

XXXII

A

Field Artillery Reference Data

XXXIII

Part 4

Field Fortifications

XI

First Aid and Field Sanitation

XXII

General Organization of Marine Corps

Artillery

XXXIII

Part 2

Infantry Antiaircraft Defense

XVIII

Jungle Warfare

XVII

LFM, Chapter XI, Interior Guard Duty and

Guard Mounting

XIII

Light Tank Tactics

XXXIV

III

A

Message Writing

IX

B

Military Discipline, Courtesies and

Customs of the Service

XV

Military Government

XLVIII

Military Principles

XXX

Military Sketching

III

c

Military Symbols and Abbreviations

III

B

NAV-5-K

XLV

B

Night Attack

XXXIX c

Notes on U.S. Marine Corps Aviation

XX

Offensive Combat of Small Infantry Units

VIII

Organization of Marine Infantry Regiment

VII

Pursuit

XXXIX

E

Raids

XXXIX

F

Reconnaissance in Force

LXIV

A

Reference Data

XXXI

B

XXXIX

A

River Crossings

LXIV

B

Sample Operations Orders

XXXII

B

Scouting and Patrolling

VI

Signal Communications in the Infantry

Regiment

IX

A

III A— 153

Title Volume

Special Operations of Infantry Units

Staff Principles and Functions

Tactical Principles

Tactics — Decisions

Technique of Rifle Fire

Terrain Appreciation

The Solution of Map Problems

U.S. Marine Corps as Component Part of

the U.S. Navy
Weapons

NOTE: The volume number corresponds to the number of the first
subcourse to which the text applies. Where a subcourse uses
more than one text, each text is designated by a letter in

12493(1) MCS QUANTICO, VA. 10-31-44--5M

XXXIX

B

XL

LXIV

C

LXIV

D

IV

B

XXXII

C

XXXI

A

I

IV

A

III A— 154

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